I'd have to say that the only time you should stop and fix, is if you're trying to get the muscle memory right for a complex passage or chord change.
If it's a performance play on, stay on beat, (try to not GRIMMACE or make a face like you just smelled a ripe fart..)
Stay cool pretend like nothing happened no one will know unless it's a major clam, and even then, maybe not. Depends on the setting, a Concert, or solo performance like recital or what ever just forget about it, the moment is gone.. In a noisy bar, or coffee house,, no one's gonna know what happened. And, you're the only one that will care.
Recording, depends on what you use. many things are very easy to do punch ins to fix mistakes. (Pro Tools for example..)
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