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

  1. Launch RealPlayer
  2. Click the RealPlayer icon in the upper left corner of the window and choose Preferences.
  3. Choose Download & Recording from the left hand panel
  4. Uncheck "Enable Web Download & Recording for these installed browsers"
  5. Click OK and close RealPlayer
  6. Restart Firefox

That fixed it for both Rose and me.