If you are a experienced Firefox user, then you probably would know about safe mode. I would launch Firefox in safe mode, then play a flash video on youtube. All youtube flash video have an option called "show info" that lets you see if the video you are watching is dropping frames.
I have an older stock q8200 quad processor, 4 gigs of ram and Win 7 64 bit with Firefox and I am not seeing any dropped frames at 720p, or 1080p for the Avatar HD trailer http://www.youtube.com/watch?v=_i2RCBa3l-g&hd=1
Used this specific clip b/c it is good benchmark trailer, being long (to test streaming performance) and with a lots of action/motion which taxes system.
And this is with my "dirty" profile or main profile with 9 extensions, and the browsing session has been on for while meaning according to task manager Firefox has accumulated more than 519,000 k of memory and that is not including the Flash plugins which is taking another 100,000 k or so and of course I have Avast Free running and all its real time modules running including the script shield patch.
I am not doubting that you are seeing what you are seeing, but I would double check your setup again to make sure Avast is really the cause.