It's common for complicated proofs to have little gaps that got past the referees. The basic standard of whether the proof is valid is that if you do find a ga

It's common for complicated proofs to have little gaps that got past the referees. The basic standard of whether the proof is valid is that if you do find a gap in the written version, the author can say "oh yeah, you can fix that by doing X", making some small patch. It's like finding a bug in a program that the author can fix right away once you file a bug report. If the author is unable to fix the bug despite a reasonable amount of effort, then there is a problem. You get credit if you can fix it where the author couldn't. Otherwise it's almost like trying to invalidate a proof over a misspelling. In the case of Wiles' proof of FLT, someone found a bug, Wiles worked unsuccessfully for something like a year trying to fix it, basically concluded that FLT was not really completely proved after all (i.e. he had "merely" made enormous progress, but not actually closed the ticket). Then right after more or less giving up, he and Richard Taylor figured out how to fix the bug, so it came out ok after all. Of course Taylor now gets a slice of the FLT credit.