Bobad, a lot of people have had trouble with Firefox too.   But it all seems to be working fine now - after about 3 days of weird glitches - and I've been able to play YouTube videos all along, with my same hardware and software. The only problems I had were in some parts of the YouTube site itself, and they've gone away without my reinstalling any software or changing browsers or adding plug-ins. So I'm guessing that, with all the people who've been commenting about this online (here & at YouTube's Help Forum & on some tech sites), the YouTube people have probably figured out what the bugs were and fixed them.   
The bugs did seem to affect only some browsers (Firefox and Safari) and were also intermittent and manifested themselves in related but not identical ways.

Anyway, for now YouTube seems to be working for me the way it always did.