MacOS – How to find more Game Center games on Mountain Lion

I am not aware of a way to force the updating other than running the apps to see if they will update things as a matter of course. Some app developers store the achievements in a way that they flow back from the game center - but it's more about how each developer chooses to use all the Game Center options.

Look for a much better experience when iCloud allows developers to store more app data in the cloud so you don't have to export/import and otherwise work to get your settings and loot to a new instance of the same app.

An alternate tack is to dive into the library of each app using a tool like PhoneView. You don't need to jailbreak the device - but often can find the folder where achievements are stored and you can put them back when they go missing.

The simplest way is to delete the game from your iPad, which will destroy any local stored game data, and will prompt you to remove the app from Game Centre (which I assume you want to do if it's corrupt on the Server). Then redownload the app (or re-add it in iTunes in your computer). This should allow you to start with a clean slate.