If you ignore a mistake that you've just made and dont correct it immediatey, your subconscience registers that mistake as the right note (your SC doesnt know the difference between a right and wrong note, just does what you've programmed it to do). If you do not correct it immediately, chances are, its there to stay. Or you'll spend far too much time practising it out again. Time that you could've spet learning the rest of he piece. Or progressing on.
As for the performing side of things... It was said earlier, that if you constantly go back every time you make a mistake while practising, you'll do it on stage aswell. Not if you can help it. If you've practised properly, and worked all the mistakes out, then you'll be fine on stage. Once, you've perfected the piece, play it through, again and again, until you've gotten used to what the piece is, as a whole. Also, when on stage, and nerves start kicking in, you automatically revert back to doing what you've done the most. (so if you've made mistakes 80% of the time, and only had it perfect 20%, you're most likely going to screw up on stage, which is why perfection repitition is so important),
As for the nerves, you only really get nervous if you are not fully prepared (unure of whether you know your music or not) If you are entirely confident that you can play every note backwards in your sleep then ther would be no point in getting nervous...