I spent so many hours wondering why my Game Center scores were not showing up. I followed all the code samples, but my callbacks were giving me ERROR: 17 for loadScores. So I never saw any scores or times that I reported to Game Center.
Well, it works now, and it had nothing to do with the code itself, but with the way Game Center works in Sandbox Mode. It was actually really easy to fix.
Make sure that you:
(1) Create a test Apple ID (appleid.apple.com) and log into Game Center in your device's Settings with that one.
(2) For all the leaderboards that exist in your profile, make your code fill them with a score. Just make sure ALL your leaderboards have a score (or time) in them.
(3) Make sure you use both your Apple IDs to populate your leaderboards with scores. I believe Game Center requires 2 users submitting scores before they become real.
All of a sudden, my scores and times started showing up.
My computer right now is OS X Yosemite (to build to device only), and iOS 7 on my iPad. Game Center doesn't work with iOS 8 Beta 1 right now.