The crazy far-out fringe media get it wrong more frequently and more comprehensively than the mainstream media; indeed, the definition of 'mainstream' implies that this will be the case - extremists are rarely a good source of information on anything.
Where do you expect people to get their news, if minor script-editing errors (such as saying 'When she signed the bill into law' instead of 'When her husband signed the bill into law') render them completely unusable? The error was not a central part of the story. It is poor form to make such errors, but it is not surprising, nor is it a big deal.
It would be nice if reporters were better educated on the subjects on which they report; but it seems likely that this example is not a factual error as such, but rather a blunder introduced by a script editor. I am sure you can find much better examples than this of real, factual errors; they are fairly common in the 'mainstream' media, and more common still elsewhere. As with all information, it is unwise to rely completely on one single source. Nobody gets it right all the time*.
* Except bilby on Talk Freethought. He is brilliant.
Of course, amateurs make all kinds of mistakes, and yes, the media makes all kinds of factual errors as well, and that is more significant. But it shouldn't happen in a professional news organization that is supposed to check and double check what it puts out. Nor was this a simple case of say "she" when she meant "he." As you've pointed out the whole phrase would have to have been re-worded.
So standards are lax at CNN, and they make mistakes. Everyone makes mistakes. That is far from being a sufficient reason to NEVER watch mainstream media; If you want checking, you need to do it yourself - as you, I, and most other people who watched the video were readily able to do.
I am struggling to see the logical steps between your evidence and your conclusion here.
1) CNN made an error in one story, whereby they incorrectly stated that the first lady (who was the focus of the story), and not the president, had signed a bill into law.
2) ???
3) You should NEVER watch mainstream media.
Would you care to make an attempt to fill the gap here? I can see how a conclusion like "People should be aware that CNN make occasional errors" would be justified; or even "People should be aware that any information source may be prone to error". Perhaps one might reasonably conclude that "I should write to CNN, pointing out the error, and ask them to tighten their standards". But "You should NEVER watch mainstream media" is a deeply flawed conclusion - particularly given that by avoiding mainstream media one exposes oneself to a greater incidence of such errors of fact, not a lesser one.