physics - 6:15 pm on Apr 2, 2008 (gmt 0)
One would be to have a feature where users can report dead videos.
A warning, though. I've found that if you leave a page open for 15 minutes and then try to play a YouTube video, it says "This video is no longer available" ... but click refresh and it's available, so watch out for that (add a refresh every 10 minutes to your pages maybe).
As far as an 'official' way to check I'm not sure.