Had the same problem
The same thing happened to me - I didn't even have any MobileMe galleries.
It took several steps, but I finally got it to shut up.
First, I used Force Quit to get out. Then, when I opened Aperture again, I clicked "Learn More" instead of telling it to move.
That opened a Safari page about the move, which I ignored. I then went to File>Web Accounts and deleted MobileMe.
After this, thought I was done. BUT, next time I opened Aperture, it told me that the library had been moved, and asked me to move the files. This time, the main window opened to what it claimed was my MobileMe Gallary, as if it was actually working. Now, though, I went to the left side, clicked and held MobileMe, and selected "Delete this account". That ended the transfer; on restarting Aperture, it finally let me work with photos without having to thread my way through prompts that would hang the application.