The completion of the classification of finite simple proofs was first announced in 1983. However, as late as 2008 minor gaps were still found and closed.
How certain can we be that
(By request, I am posting my earlier comment as an answer to remove this question from the unanswered queue.)
We’re pretty sure. This is a good read on the status by Aschbacher. At this point, we’re trying to simplify the proof because it’s pretty messy and not very elegant, not because we aren’t sure that it’s correct.