I'm not sure if this will help, but I used to have a similar problem with other video services like Hulu and Yahoo. Their videos would never play, but Youtube did. And to make things even weirder, I never had problems if I used Firefox or Chrome.
Anyway, I reinstalled Flash and uninstalled it many times with no luck. I finally was able to narrow it down to some sort of incompatibility between 64-bit mode and 32-bit mode in Flash with Safari. I run everything in 64-bit mode, but I guess Flash was in 32-bit mode or something. I went to the Get Info window of Safari (right click Safari> Get Info) and ticked the "Open in 32-bit mode" and it worked. Now all my videos on all services work.
Hope this helps.