And then there are some days where your fingers completely betray you, and you have to make that split second call of "Do I stop the recording and start over, or keep going?"
I kept going.
One of my goals with the improvs is to work on my "recovery" skills. With me, f***-ups are inevitable whenever I'm near a piano. So recovery skills are what I use whenever I do screw up.
Though I've yet to play piano live, I do entertain the notion that some day I may get the opportunity to do so.
So, here's how I see improvs helping:
The obvious is that, if you set a goal to just keep going no matter what, you're playing by the same standards that would be expected in a live situation.
Granted, this one applies more so to solo live performers, but by developing improv skills in general, you learn how to cover up your mistakes by playing something that complements the screw up.
So for #2, say you hit the wrong chord. If you're lucky, the chord still fits enough that all you need to do now is tweak the melody enough that it complements the new (incorrect) chord. And if you're really good, you can turn an out-of-place chord into a clever tangent.
Alternately, you can just keep going with the clashing things and get back to the intended music as soon as you can. A lot of people may not even notice.
Just keep going.
Alternatively, be more like Tori Amos and f*ck it up, but be charming.