It’s been driving me mad. For the past few weeks, I’ve been trying to watch youtube videos (Educational stuff – not the skateboarding dog – although that is pretty neat…) and been plagued with flickering video playback.
I was also getting flickering when using Compiz desktop effects.
Finally, after a couple of headaches, I researched the problem. Turns out it looks like an incompatibility between my ATI X1900GT card’s drivers and the way Compiz tries to use it. Something to do with an unsupported call making the application use unaccelerated rendering (and all your CPU resources), but at least I now have a fix – turn off desktop effects.
System > Preferences > Appearance > Visual Effects Tab
Select ‘None’, then ‘Close’.
Et voila – no more flickering.
It’s a shame you can’t have the simply beautiful effects AND flicker-free video playback. If anyone’s got a better answer, please leave me a comment, but for now, my advice? If you have the choice and you want an easy Linux life, buy nvidia. My nvidia mobile-based laptop works a treat.
(I did try an alternative solution, adding Option “TexturedVideo” “off” to my /etc/X11/xorg.conf, but it didn’t really work for me – less flickering, but still there.)
Now, back to that skateboarding dog. I mean educational material…
crossedstreams.com 
A friend of mine was having this problem yesterday – I’ll point him here to see if it helps.
Like you, I have no problems with Ubuntu and an Nvidia card.
Cheers,
Mike