It depens on the mistake.
One time I messed up a card trick and ended up revealing a 5 of clubs when the selected card was a 10. I said something like "This is the half-right trick, wanna see the full version?".
If I don't get that lucky, I just ask "What was your card?", the run through the deck and cull that card to the top or bottom (discreetly) and perform some sort of colour change, changing the wrong card into the right one. Never fails.
Also, I do a lot of tricks where I intentionally mess up, so after a few of those people assume that all my mistakes are on purpose! I then fix it up and move right along.
If I flash something that the audience is not supposed to see, like a face up card in the middle of the deck, I say something like "What's this doing here?", toss the cards out and do some other trick.
Just use your imagination
