Considered from the outside, i.e., in relation only to the surface of the sound, a wrong note is simply a mistake. Attended to with comprehension a wrong note yields potentially profound insight into form, structure, musical essence.
The potential lies in the ear of the listener. Ideally one listens to one's own playing with insight but this is extremely difficult if one has not learned to do so, a skill one learns by being listened to at this depth. Herein lies the real basis of the social aspect of music--not, as I used to think, in the fact that the performance of music implies a contract between composer, performer and audience.
An interview with author/jazz musician James McBride in last Sunday's New York Times Book Review hits on a perfect example of such precision: "If you're playing a solo in the key of B flat and play, say, an F sharp or B natural, you better have a good reason for it--or be Charlie Parker."
Or Beethoven.
Read the whole interview at www.nytimes.com/books.