If you have ClickToFlash installed, you may have seen a note telling you that you have an old version of Flash and encouraging you to upgrade.
As you might expect, you don't need to upgrade Flash, but you do need to upgrade ClickToFlash. The current version is ClickToFlash-1.6b7-upload1.zip, but you may have go to the Github page for ClickToFlash to download it.
Jonathan Rentzsch explained that he hasn't been able to update it himself due to illness. However, given that it is open-source, four others (identified as ndfred, Justin, ssp and lapcat) identified the problem and a solution, and Rentzsch merged it back into the main branch of the code.
That's pretty awesome, if you ask me.
So if you've run into this problem at YouTube, take a few minutes, download the new version, quit Safari, and run the installer. Voilà!