Q: Game Center. Stuck at the saving screen.

Same question. I just updated to Mountain Lion.

Maybe this will help:

Game Center - Using/Troubleshooting

That doesn't help for me.

If the above doesn't work, quit Game Center and try the following.

You need to look in your user Library/Preferences for the .plist, which I think is gamed.

Hold down the option key while using the Finder "Go To Folder" command. Enter ~/Library. Transfer the .plist(s) to the desktop (in case it's not the right one and you need to put it back).

Open Game Center and try to log in. If the log in is successful, you can probably trash the one on the desk top if you look in Preferences and a new one has been generated.

If you prefer to make your user library permanently visible, use the Terminal command found below. It does work with Mountain Lion:

http://osxdaily.com/2011/07/22/access-user-library-folder-in-os-x-lion/

You might want to bookmark the command. I had to use it again after I installed 10.8.2. I have also been informed that if you drag the user library to Finder it will remain visible.

Same problem for me...

same thing , just bought a new macbook and first time on mac and had this problem . this is a bad first impression

Try a different name . something thats not in common . it did work for me