Stop worrying about it and just carry on. It probably doesn't matter nearly as much as you think. If it's a minor mistake, the chances are most of the audience didn't notice, or if they did they will immediately have forgotten. In those situations, the worst thing you can do is draw their attention to it, whether by pulling a face or by stopping altogether.

If it's so bad or so obvious that you can't ignore it, then laugh about it. It gets the audience on your side.

It partly depends on what's caused the mistake. If you forget the tune, there's not much to be done about that, although practice will improve your memory retention and maybe help you find tricks to recover a llost tune. You can bluff, if you're sufficiently familiar with the genre to improvise a tune or make up missing words. If the mistake is simply due to incorrect fingering, untangle them and get back on track - again, the ability to improvise will help you over this.

If you can keep the rhythm going and make it appear that music is happening (so avoid vamping bar after bar of the same chord while gazing at the ceiling for inspiration) you can usually get away with it. That's what I tell myself, anyway.