It appears that YouTube has changed the way that their embedding works, and perhaps they have also changed their API.
Videos used to be embedded in an iframe using the following protocol: http://youtube.com/embed/http://youtube.com/v/videoIDgoesHere
While this may not have been the most elegant solution, it worked perfectly for thousands of people who use this particular YouTube plugin within a text editor.
Now, the embeds work like this: http://youtube.com/embed/videoIDgoesHere
Also, the following type of link: http://youtube.com/v/videoIDgoesHere now redirects to Google's API.
Videos can once again be embedded, but all existing YouTube videos will need to be replaced. Youtube has not announced a change, and I'm wondering why developers were not warned. Had I known this would happen I could have initiated a change before all existing videos on TopicSpotter were redirected to a 404 error page.
For those interested, TopicSpotter is now using the Google API method (http://youtube.com/v/videoIDgoesHere) instead of the embed method (http://youtube.com/embed/videoIDgoesHere) in order to avoid another issue with the embed API.
I'm very sorry for the hassle.