Game Center corruption. How to fix? Lately I'm finding that I am not able to use any software that utilizes Game Center. In iOS 6 on login (or opening any game) it says, "Could not connect to Game Center server." In OS X Mountain Lion on login, it says, "The data couldn’t be read because it has been corrupted."

I've tried some steps to fix that were suggested in Apple's Support Discussions without success. These include rebuilding permissions, resetting PRAM, restoring the /etc/hosts file to its default state, and in OS X, logging in using Chess instead of Game Center.

That this is happening on both of my devices (MacBook Pro and iPhone 4S) makes me think the 'corruption' is occurring on Apple end, in the cloud. I'm wondering if anyone has experienced this issue and conquered it, or if Apple Support can do anything to restore this functionality on their end at a customer's request.
I'm thinking that the server just must be down. I'm having the same issues logging into my game center on my iphone 4s. Perhaps it will fix itself within the hour as things like this apparently have happened before.