Game Center in Mountain Lion won't let me log in I'm trying to log in to Game Center using my Apple ID but it just won't let me do it. Actually, nothing happens: no error messages, just nothing.

I think there is an issue, because I also get a pop-up window where I suppose a new registration could be done within the same program, but it's blank (Annulla means Cancel):



Apart from what is being suggested in this question about Chess over Game Center, why isn't the simple log in working? I could use the workaround but I want the standard way to work anyways.
I had a similar problem. For me, there was a verification screen that popped up behind the login screen. I could not see it at all! Not sure why I thought of it, but dragging the frontmost window out of the way showed me the verification screen, I did what needed to be done there, and on I went to Game Center to be underwhelmed.