I upgraded to iOS 6 and now when I check the Game Center leaderboard from my game, there is the empty outline of a Like button right next to the Tap To Rate This Game stars, which says “Facebook Liking Unavailable.”
So of course if Facebook liking could be available then I want it to be. No help from Apple there- I already searched on the iOS Developer site, and their site search is useless.
Had the same issue - but solved it. In order for it to work - you must sign into facebook on your iOS 6 device. Settings/Facebook then sign in. It will work after that. Hope that helps!
Does it really take you to some Facebook page or does the like button in game center just
create a “like” post on your own Facebook page… which would explain why the like button
in game center only displays when you are logged in your own Facebook-account