I have noticed that for some reason with the new flash-player it runs two of them in the task manager processes.
If you go into the task manager, then click on the processes tab and then see if there are two flashplayerplugin.exe running, if so right click on the one with the highest usage of memory and end process. Then if you refresh the page your YouTube video should play fine.
That is only the quick fix I have been using, not sure if there is a permanent fix.