Why can't I upload videos on to YouTube without getting this message all of a sudden "Publishing to YouTube Failed: The operation couldn’t be completed. (Unauthorized)"?

While this seems to be a Youtube issue (not Apple) I would recommend updating Flash and see if that seems to help. Navigate to Adobe's website and update directly from there.

If that doesn't work try this: In iMovie go File->Share->File then save it to your desktop. Once there go to the You Tube site directly and upload it from your desktop. That should work. You Tube will prompt you if there is any issue on their end, such as you need to create a channel or whatever. Hope that helps.