Question: What do you mean by "mistakes are 'unwelcome guests' and we are to check them at the door" (quotation from your Piano Practice page)?
Albert's reply: One of my teachers once asked me to imagine that every time I made a mistake in practice, a trap door underneath the piano bench would open up and I would fall into a pit of alligators, never to be heard from again! While this analogy may sound extreme, it reveals the enormous care with which we are to go about our business of practicing.
Our brain is a perfect digital recorder that will reproduce anything we feed it. If we practice mistakes, we learn mistakes. If we practice accurately and beautifully, we learn to play accurately and beautifully. It's that simple.
Many amateurs assume that it's acceptable for them to make mistakes while practicing, because they're amateurs and are playing for their own enjoyment after all. Yet observe their frustration each time they make a mistake!
This is the mental aspect of piano technique. Rendering each musical motive, each accompaniment, each melody as perfectly as possible is far less a matter of finger agility than it is concentration.
Nonetheless, no player is immune to mistakes. I wrote a lesson titled Insecurity and Mistakes, in which I offer a formula for dealing with the inevitable mistake.
For all the hyperbole about accuracy (no one will get eaten alive by alligators for playing a wrong note), we are human, and high art, for all its striving for perfection, is ultimately among the greatest expressions of our humanity. As craftsmen, we must prepare all our music as carefully as possible so they we may express it as beautifully and freely as possible. The goal of a performance is to communicate—no one wins by getting through a piece with the fewest wrong notes, but by expressing the underlying music.