How to Make a Mistake Go Away Fast

The fastest way to make it go away is just to forget about it and not do anything about it. So then the challenge would be, how can you help somebody else see a mistake and at that moment offer them something better to do with it than look away? Some sort of a hook by which they could update something else about their beliefs about themselves. They don't want to stay in this position very long because they've got some easy outs like making up a new theory.