How confident can we be about the validity of the classification of finite simple groups?

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

  1. The proof of the classification theorem is correct
  2. Even though there may be mistakes in the proof, at least the result is correct, i. e. our list of finite simple groups is the right one?

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