its nothing to do with Java or anything, these folks know nothing.
its Youtube only, and will affect you based on which video chipset you have.
Nvidia seem to be unaffected so far. its affecting many Linux users and as we see, some Mac users. for the last few months Youtube now owned by Google, have been taking measures, (it is thought) to stop or to make difficult for people to illegally download protected material, and of course Linux and Mac users are further down the ladder.

the disable cookies seems popular, but disables the ability to login to Youtube.

In Firefox there is a fun little plugin (add-ons) called FlashVideoReplacer
which forces Youtube videos to play in a proper media player. VLC, Kplayer, KMPlayer, Smplayer Kaffeine, Xine, Mplayer, Totem Dragonplayer or whatever. all work,
but " FlashVideoReplacer " seems a little flaky on my system so far. i even uninstalled
Flash to test, and Youtube was sweet. interesting.

Also possibly reverting to to an older version of Flash is possible, but i've not tested that as i am ignoring Youtube until they fix it.