The recent upgrade to Adobe Flash has been doing a hit job on FireFox. It causes videos (youtube, etc.) to attempt to load, but fail.
Firefox 13 has its own problems, too, however.
I went back to FF12 and found that Adobe Flash 10 will work with it. But Adobe Flash requires ver 11 for IE9. [Both Flash versions can be installed — just install 10 for FF, but install 11 for IE.]
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Too many times, upgrades and updates create more problems than they fix.
I agree the upgrade schedule for FF is ruining it. I had issues with memory leaks with FF for awhile but it seemed that after they fixed that issues it started being more unstable and tabs crashing. Adobe was a prime culprit in that as well as scripts. I will give FF this though, if Adobe crashes you can simply reload the tab and not restart the browser like you would with Chrome.
I find that viewing videos in HTML5 works better. For Youtube, you opt-in to the HTML5 Trial, and most, if not all, of your Youtube videos will then be served in HTML5.