So, it looks like this research started back in 2016, with a paper in the Astronomical Journal by 
Villarroel, Imaz & Bergstedt, entitled "Our Sky Now and Then: Searches for Lost Stars and Impossible Effects as Probes of Advanced Extraterrestrial Civilizations". In that paper they propose "searching for physically impossible effects caused by highly advanced technology by carrying out a search for disappearing galaxies and Milky Way stars."  The idea was to search images between sky surveys taken at different epochs and look for disappearing sources. 
[quote = Villarreol et al. 2016]
In this paper, we propose replacing the search for possible signatures of astroengineering with a search for impossible (or nearly impossible) effects for conventional astrophysics. Quoting Arthur C. Clarke’s Third Law, “Any sufficiently advanced technology is indistinguishable from magic.” Examples of such hypothetical effects include a galaxy that rapidly and strongly changes redshift or apparent size over the course of a few years, or a galaxy, previously visible on the sky, that suddenly disappears 
entirely from its location. Also, a Milky Way star that disappears entirely without an accompanying supernovae is equally interesting and can indicate the existence of an advanced extraterrestrial civilization with an interest in hiding a star from their enemy. However, it can also point toward unknown or exotic physics, like stars disappearing into wormholes.[/quote]
They use the United States Naval Observatory (USNO) B1.0 catalog, and include objects that were also detected in two epochs of the Palomar Observatory Sky Surveys (POSS). They then matched these against the Sloan Digital Sky Survey and search for objects that have disappeared. In the end they found one candidate, "though an uncertain one due to its faintness in POSS-2. An improved image analysis is needed to determine with confidence whether it is a real detection, as was originally reported in USNO-B1.0."  They claim that if it is real, it could be something natural that could be discovered with follow-up studies by more powerful telescopes, but if it is not found by those, then it "opens up the opportunity for fascinating, new interpretations."
It then seems that Villarroel got very interested in looking for more things in the POSS plates and, in 2020, wrote another paper for the Astronomical Journal entitled 
'The Vanishing and Appearing Sources during a Century of Observations Project. I. USNO Objects Missing in Modern Sky Surveys and Follow-up Observations of a “Missing Star”', starting the so-called "VASCO" program. In this research they compare the USNO-B1.0 survey to a more recent Pan-STARRS survey. They followed up the 2016 detection with new observations in 2018 and did not find it. They do address the idea that it could have been a plate defect, though admit they do not have access to the original plates, so have not examined them. 
They decide to examine the point spread function (PSF) of the source to stars in the field, suggesting that objects with PSFs considerably smaller than stars "may be discarded as a plate flaw." They state that their object "appears to be like many astronomical point sources and has a PSF comparable to the real stars on the plate. This suggests that it is not a plate defect." In their discussion section they give potential possibilities for why it was detected once and never observed again and ultimately admit that "Since only one secure detection of these objects [sic] exists, and although that detection seems to be of a point source, it is difficult to establish its nature."
Continuing to identify mismatches between the Pan-STARRS survey to the USNO sample, they ultimately, after ruling our "artifacts of various sorts" end up with a sample of about 100 candidates visible only in the POSS plates (taken in the 1950s to 1970s). They do go on to state that:
[quote = Villarroel et al. 2020]
Undoubtedly, VASCO will generate large lists of candidate objects in searches for vanishing stars. Individually, these serve no purpose unless verified. We can agree that a wide-field search that results in a list of candidates is of no great interest for research if each candidate sooner or later gets dismissed due to a lack of verification as a potential SETI candidate.[/quote]
In 2021, 
Villarroel, et al. wrote a paper in Scientific Reports entitled "Eploring Nine Simultaneously Occurring Transients on April 12th 1950".  It seems they have gotten in deep with the POSS scans, looking for even more unexplainable sources. They give explanations as to why they might rule out various phenomena, but ultimately admit that one possible explanation is that "the plates have been subjected to an unknown type of contamination", but also suggest that if they can exclude contamination, "another possibility is fast (t  < 0.5 s) solar reflections from objects near geosynchronous orbits."  These would have to be very short glints or they would appear as streaks in observations that were taken at sidereal rates for astronomical observations.
There was a paper by 
Solano, Villarroel & Rodrigo in 2022, published in the Monthly Notices of the Royal Astronomical Society (MNRAS), entitled "Discovering vanishing objects in POSS I red images using the Virtual Observatory" that puts together a sample of sources only visible in the POSS-I plates. They end up with 5399 unidentified transits, after ruling out asteroids, variable objects, high proper motion objects, and artifacts. They point out that "Working with POSS I data has the advantage of getting rid from contamination of artificial satellites and, at the same time, opens the possibility of exploring long-term (of the order of decades) variability phenomena."
They conclude that:
[quote = Solano et al. 2022]
Although the origin of these 5399 vanishing sources is not clear, most of them might be associated to large amplitude (> 2.5 mag) variable stars like, for instance, flare stars. Other physical (unknown asteroids, non-catalogued high proper motion objects or exotic objects theoretically proposed like failed supernovae) and artificial (technosignatures) mechanisms can also be proposed to explain the disappearance of our list of objects in modern archives.[/quote]
In 2024, there was a paper by 
Hambly & Blair, published in the RAS Techniques and Instruments journal. In this paper, they "examine critically recent claims for the presence of above-atmosphere optical transients in publicly available digitized scans of" the POSS plates. I haven't read the details of this study, but they point out a few things:
[quote = Hambly & Blair]
Neither Villarroel et al. (2021) nor any of the follow-up works discuss the provenance of the photographic plate material scanned in creating the images on which their analyses are based yet the reproduction of glass copy plates from the survey originals is clearly an important consideration.[/quote]
This seems to be a very important point. If Villarroel really wants to rule out plate defects, she should look at the original plates. She has commented in more than one of her paper that they have not done so or appear to have made an attempt to do so. After ten years of study you would think this should be a priority.  
Hambly & Blair conclude:
[quote = Hambly & Blair]
We find that (i) the image profiles of the transients are significantly sharper than typical stellar images on the plates; (ii) that an ML decision-tree classifier badges the images as spurious with high probability; (iii) that similar examples of apparent transients are present on the copy plate of the adjacent field; and finally (iv) that there are many hundreds of similar images on both plates in the overlap region between the two fields. We suggest one likely mechanism for the origin of at least some of these apparent transients as being emulsion holes on the intermediate positive plates used during reproduction of the copy sets. We therefore caution that digitized all-sky survey catalogues derived from the POSSI glass copies are likely peppered with these isolated false detections and that great care must be exercised when interpreting the publicly available digitized images or when making samples of unpaired catalogue records derived from them.[/quote]
Now, this most recent paper, which is getting the attention (along with the one written by the anesthesiologist), is entitled 
"Aligned, Multiple-transient Events in the First Palomar Sky Survey", by Villarroel et al. and just published (October 2025) in the journal Publications of the Astronomical Society of the Pacific (PASP). In this paper they address two specific studies: 1) looking for transients that appear in a line in the POSS plates, and 2) examining the statistics of transients that appear in the Earth's shadow. It seems they are pursuing this idea that short flashes of sun glints from objects could result in these "aligned" transients and if it is due to the sun then there should be a dearth of them in observations that include the Earth's shadow. 
They directly address Hambly & Blair's conclusions that the artifacts "are likely emulsion artifacts". Villarroel et al. state that Hambly & Blair based this on the slightly narrower full-width-at-half-maximum (FWHM) values of the artifacts compared to normal stars. It's not clear to me that that was all they based their conclusions on, but I admit to not having fully read or understood the Hambly & Blair papers. Villarroel indicates a few possibilities as to why the transients might have narrower FWHMs. These include: 1) non-linearity of photographic emulsions, "which causes fainter sources to naturally exhibit narrower profiles", and 2) that "sub-second optical flashes are predicted—on physical grounds—to appear sharper and more circular than stars in long-exposure plates, due to the absence of atmospheric seeing, wind shake, and tracking-induced smearing." I don't know much about non-linearity of photographic emulsions, but the second statement is largely true.
Villarroel then do two things: look for transients with a "roughly linear arrangement" of three or more objects, and also performed a statistical analysis of the relative populations of transients in and out of the Earth's shadow, both utilizing the sample from the Solano et al. (2022) paper.  However, they state that they "base [their] analysis on the catalog of 298,165 short-duration transients presented in Solano et al. (2022)". This seems odd to me because Solano et al. already concluded that they only had 5399 unidentified sources. So, it would seem that this analysis could be contaminated by known sources.  
For the linear arrangements, they identify five "most interesting candidates" that have at least three linearly aligned transients (and possibly four or more if they widen the criteria for 'alignment', which kind of makes them not quite so linear anymore).  After doing a statistical analysis, they conclude:
[quote = Villarroel et al. 2025]
...we see that all 3-point alignments are non-interesting events with 
p > 0.05 (less significant than 2
σ), with an exception of the borderline case of Candidate 2. This shows that for POSS-I data where the seeing in general is rather large, 3-point alignments of simultaneous transients do not provide significant proof against randomness. The interesting cases are the 4-point and 5-point cases, namely Candidates 3, 4 and 5. Yet, one could argue that without an inspection with a microscope one still cannot exclude plate defects.[/quote]
The 4-point and 5-point cases are not really quite linear, if you examine the images provided in their paper, so I'm less impressed with the possibility of those being flashes from a single object. 
They get into a bit of the UFO stuff with the following quote:
	
	
		
		
			However, what makes the events even more interesting is that Candidate 5 occurs on the same date as one of the most famous UFO mass sightings in history—namely, the 1952 Washington UFO flap (Villarroel 2024). This could be a coincidence. We also note that Candidate 1 occurs within a day of the peak of the 1954 UFO wave. We shall discuss this further in Section 
10. These additional two coincidences further motivate scrutiny of the plate defect hypothesis, especially in light of the combined statistical and contextual factors presented in this study.
		
 
I find it a bit misleading since they already ruled out Candidate 1 as a "non-interesting event".
There's a section assessing conventional explanations and one they rule out is optical ghosts, stating that "Ghosts typically exhibit extended or clumpy morphologies and do not match stellar point spread functions (PSFs)."  That is generally true, though there are definitely ways to have in-focus ghosts, and I myself have seen those with systems I have used. But they probably aren't ghosts, I would agree. They address the defects with the FWHM argument stated above. 
They then have a statistical analysis of transients in the Earth's shadow and I admit to not being an expert in statistics so don't really know what to make of it. It's a good approach to discern between plate artifacts, which should not intrinsically show a bias for when a given plate is observing into the Earth's shadow, so if their analysis shows a true statistically significant effect that is quite interesting. As stated earlier, I am concerned that they used the full Solano et al. (2022) sample, instead of the subsample (5399 objects). 
Finally, they talk about kinds of shapes of objects that could cause short glints and speculate way outside of the merits here. They do recognize that the "geometric models presented in this section are intended to demonstrate the plausibility of producing aligned glint patterns from tumbling or precessing objects in high-altitude orbits. We emphasize that these models are illustrative rather than predictive, and no attempt is made to fit the specific time separations or angular offsets of the individual candidates."
Well, that's the bulk of the history as I'm willing to dig into right now. I won't address the anesthesiologist's study. I think Villarroel has attempted to take on this subject with as much scientific rigor as befitting a professional astronomer. There's nothing intrinsically wrong with any of these papers. However, given the nature of the claim, I would think there would have to be quite substantial evidence to run out plate defects, and it's disappointing that they continue to point out that much would be gained from "microscopic examination of the original plates" but do not report on any efforts to do so.
So, in conclusion, these observations could just be plate defects and if you dig deep enough into any very large dataset you're bound to find a few unexplainable things. It seems a stretch to try to identify these with non-terrestrial objects, which could lead you to making unfalsifiable claims (such as explaining away the shortness of the glints by unverifiable geometries of putative objects). 
Carl Sagan said it best: "extraordinary claims require extraordinary evidence".  In my opinion, the evidence has reached that standard.