Same to me. 9790 with BlackBerry OS 7.1. 2-3 days ago I am unable to watch Youtube videos. Haven't tested with Facebook. As long as I observed, problem is the browser don't detect the picture being a link, so I can't click it and so the media player does not start.
For me this is an issue with either the mobile version of Youtube or the Youtube "plug-in" or whatever that thing is which deploys into the browser to let us see the Youtube videos.
Yeah, after I replied here and saw the other tread with the 4 page posts about this issue. But BB have to write their own player or they will suffer waiting the mercy of Google, which is in the favor of Android.