I love mistakes. In music anyway. In real life they can cause anything from mild annoyance to a life-threatening issue. But in music (more importantly, improvised music) they are, as far as I'm concerned, an absolute necessity. Music with mistakes makes it human. No one is perfect. That's probably why I've always shied away from electronic music or any kind of music made with a computer. No matter how brilliant the composition is, I always feel that there is something lacking: that human element. I'm not putting down that style of music, it has just never really resonated with me. Mistakes to me imply that a player is reaching for something just beyond what he/she knows. It means they are stretching, aiming for something in their improvisation that may or may not work, and may also be beyond their technical means. Which is both exciting for the listener, and a great teaching moment for the player. Good players learn from their mistakes, and use them to grow as a musician.
Jim Hall explains it perfectly in his fantastic book 'Exploring Jazz Guitar':
'You are presented with a pile of rocks. You have the opportunity to construct something with them - a free standing wall or maybe an archway in a wall. The wall is the easier of the two (aside from the rock-lifting) because it involves finding rocks that fit one another to form the wall, big ones on the bottom, smaller ones toward the top. An arch is a different matter: it has tension and drama and contains the possibility that it may fall on itself, fall to the ground and become a pile of rocks again. Chance taking, and sometimes missing is a big part of the fun of improvising: taking the chance that your solo may fall in on itself, just like the arch of the stone mason. That has happened to all of us at one time or another, and needs to happen more frequently.'
I recently did a gig consisting entirely of Woody Shaw tunes. It was something I had dreamed of trying for awhile, and I had somehow tricked some amazing musicians into playing with me. And I worked hard on those songs for months. The gig was so much fun, and for all intents and purposes a success. And I made a ton of mistakes. A few owing to the tendonitis in my forearms, some others to my nervousness. But the majority were because I was trying to play things above what I know.
The musicians I hired (Ben Markley and Ron Coulter) are so good and inspiring to play with I felt that no matter what I tried, they had my back. And, except for a few clams, I'm sure the audience had no idea that the line I just played had completely fallen apart. My arch had fallen in on itself. But the audience isn't in your head: they have no idea what you are going to play next. To them it sounds like it was all part of your plan. You know better, and hopefully have the presence of mind to remember that fallen archway and work on it later in your practicing.
So embrace your mistakes. Treat them as teaching points. I've often said that the music I find most enjoyable to listen to (and to play) is music that sounds like at any point it could fall apart. Like that stone archway. Luckily, we get to deal in notes and chords, not rocks and stones. There is less chance that our mistakes will have any kind of catastrophic consequence to them. Don't be afraid, it's only music. Reach for things just out of your grasp. Build the arch, not the wall. I summed all of this up for myself with this phrase: If you're not failing, you're not trying hard enough.