This sounds like a problem with the Flash player. you can edit the flash player's settings by going to:
In the section "Website Storage Settings", increasing the amount of data youtube.com can store on your computer might help. Completely deleting youtube.com from the list of visited websites might also help (since that might get rid of any corrupt data).
If that doesn't work you can also try deleting the flash player's cache files manually.
just delete all the folders out of:
/Users/[YOUR USER NAME]/Library/Caches/Adobe/Flash Player/AssetCache
The folders should have names that look similar to "5PXNHG84" or "KK4Y5DSK".
Unfortunately, Flash for OS X (and linux) has never seemed to work as well as it does on windows. So what I just described still may not solve your problem, but it's worth a shot.