I've had the same issue. It has nothing to do with the disc, for starters, apparently its got something to do with the hard drive.
A lot of people had suggested that it is the update. I tried deleting it and resinstalling, and that didnt work
A lot of people had suggested deleting your system cache. I tried that, didn't work.
A lot of people had suggested installing the game to the hard drive. Tried that, doesn't install properly because the disc is apparently "dirty", or "scratched
Apparently the only fix (from what i have read) is to take your hard drive out and sign out, and than play. But i cant do this because i got the new slim :/
My only option left now is to wait for a future patch for this issue.