I was having the same issues: no YouTube videos. I went a bit deeper and found that videos I had watched before was playing just fine.
Installed the "latest and greatest" flash player. The problem with YouTube continued.
Opened up Firefox and went to a video that was causing the issue (blank video area, comment area always "loading"). It played fine. Stopped the video after the ad and about a minute of the actual video.
Then I quit Firefox and went into Safari and hit that video that was giving me issues. It began playing right where I left off in Firefox. Okay, I know that when I sign into my google account, and go to YouTube, it keeps track of what I watch and allows me to switch platforms/apps and continue to watch the video where I left off.
I had a hunch, I went to another video that was causing me issues and the issue persisted. Went to my home page (top sites) in Safari. Quit Safari. Opened Firefox and went to that video in youTube and sure enough, there was an ad at the beginning of it. Played the ad till I could skip the darn thing and played a minute of the video. Quit Firefox and opened Safari, went to YouTube and in my history, went to that video. It played.
So my takeaway is that there's something askew with the Ads that precede the videos. Safari doesn't "like" them or some such. And since most ads are in flash format, I would hazard a guess that the ads are doing "something" that is stalling Safari.