Not all "good evidence" is equal.
Is “good evidence” a subjective or objective determination?
Objective. But that doesn't mean everyone agrees in all cases whether the evidence is good. Perhaps such disagreement could be resolved if enough time or effort is spent trying to resolve it, but that might be impractical so that there'd never be agreement that it is or isn't good evidence. But even so each person's judgment whether it's good evidence is an objective determination, and this could be mistaken but is more reliable than a subjective determination.
Different groups of people can look at the exact same data and infer different conclusions from it. In religion, a Christian can point to nature and sincerely believe it is “good evidence” for God. I can sincerely believe it is not.
That could probably be resolved, with both sides finally agreeing that we don't know, or that it can't be proved, or that maybe "God" is some kind of real possibility which cannot be proved with certainty. It's reasonable as a possibility, but it cannot be proved -- or there's reason to believe it but also doubt it, or it's a reasonable hope, because of the evidence, which is better than if there were no evidence at all, and one can reasonably believe or disbelieve, based on the same limited evidence (believe because there's evidence, but disbelieve because the evidence is limited or not "good" enough).
Is that disagreement because what constitutes sufficient evidence or good evidence is subjective to each individual? Or is there an objective standard that neither of us are able to explicitly state?
The latter, usually. And you could explicitly state the objective standard, and agree, if you'd both argue the question long enough (which is unlikely). To reach this agreement probably both sides would have to modify slightly but end up figuring that their original belief was approximately true anyway, but made better with the modification.
In our current culture there's usually not enough spare time for disputants to stay at it long enough to find a reasonable resolution. And also at some point they decide that it no longer matters anyway.
Different members of a jury can each subjectively agree that the evidence is good or not good enough to warrant convicting the defendant of the crime.
Maybe it's not the evidence they disagree about, but the meaning of "beyond a reasonable doubt" or other standard required to convict. But if it's the evidence -- whether it's "objective" or good evidence -- and they have all the information, then they should finally be able to resolve whether it's good evidence or not. But probably they are not willing to go at it long enough to resolve it. Probably there's a personal animosity preventing them from arguing long enough to resolve it.
The vast majority of legal cases are much more easily resolved than this kind where the jurors cannot agree on the merit of the evidence. Most cases are resolved using "good evidence" and without even going to court.
However, are there ever cases where what is “good evidence” is indeed an objective matter?
Yes. Probably most.
Or is it inherently subjective?
No. Usually objective.
It may be intersubjective. A group of medical experts can come to agreement that a certain drug will be effective on 90% of patients. Whether 90% constitutes “good evidence” that the drug works is a subjective determination still.
Maybe, but that it's
better evidence than only 80% is an OBJECTIVE determination (if the 80% or 90% is established).
What's right is that a higher probability is
better evidence and makes a stronger case, and stronger does matter. Even if "good evidence" is problematic, drawing an artificial line between "good" and "not good," still "better evidence" is not problematic and is also important in truth-seeking.
We can objectively assess a 51% probability for a certain event to happen, but to take the next step and say that the probability is a “good probability” or “good evidence” is where it becomes subjective.
No, because "good" probably means better enough to decide the issue. But 90% is preferable to 51%. So one could reasonably judge that 51% isn't good enough.
Some legitimate decisions by those responsible could be based on only 51% or even less probability.
You could say there is subjectivity involved, but still it's objectively the case that a higher probability is "better evidence" than a lower probability. And "better" does matter and can decide an important issue -- even the most important issues.
What is an important issue or judgment which cannot be decided based on "better evidence"?
When there's an "impasse" it usually could be resolved. Today's communicating mechanisms to resolve it may not be sufficient yet, but they could be improved, and today's mechanisms are better than those 1000 years ago.
It is seldom that an important issue has to be left unresolved simply because it's "subjective" -- rather, the reason it can't be resolved is that it would take too long, and of course the usual lack of information might leave too much uncertainty. It's usually not because the opposing sides have contradictory "feelings" or "vibes" about it or are "wired" differently.