Rose and I both experienced this problem today. After an automatic update to Firefox 13.0, we couldn't watch YouTube videos. We would just get a message that says "An error has occurred." After a little googling about, I found this article which explained that there was a compatibility problem with RealPlayer. All I had to do was this:
Turn off Web Download & Recording in RealPlayer
- Launch RealPlayer
- Click the RealPlayer icon in the upper left corner of the window and choose Preferences.
- Choose Download & Recording from the left hand panel
- Uncheck "Enable Web Download & Recording for these installed browsers"
- Click OK and close RealPlayer
- Restart Firefox
That fixed it for both Rose and me.