An audience is willing to forgive and forget an error in a performance if you keep your cool and pretend everything is okay. The audience sees that you’re relaxed and become relaxed in the process, even if you’re missing every note.
They will, however, notice if you strain yourself, mutter curses under your breath, and make grimaces. The audience sees that you’re uncomfortable and become uncomfortable in the process, even if you’re hitting every note.
I think this observation deals with the phenomena of listening with our eyes. In judging a musical performance, we not only focus on the way the performer presents the music but the way she presents herself.
What can we do with this realization? For me, one thing is learning how to make mistakes. It sounds odd at first, but we’re so used to crumpling under the pressure of a mistake and resorting to distress. That only hurts a performance. Keeping relaxed during mistakes can only be beneficial to music making.
The audience will certainly hear the difference. They’ll be all eyes and ears.