YouTube has been telling me for weeks now that I have 1 unread private message, but there was no message! It was pretty annoying, and it took me forever, but I finally found a solution. I'll post it here, just in case this happens to anyone else.
1. Open two windows (or tabs) of your YouTube Messages page.
2. In one window, send a message to yourself.
3. After sending the message, refresh both windows.
4. Open and close that message in one window ONLY click on the comments tab. Refresh that window ONLY.
5. On the other window, open and close the message, then click the comments tab.
6. Smile in glee at the fact that you no longer have an "invisible" YouTube message!