I know it sounds counter intuitive at best and crazy at worst, but it is true that mistakes are beneficial to make when you are learning to play the piano. So often we are trying to avoid mistakes because it is the mistakes that makes our playing flawed, but really it is making mistakes that we can improve our knowledge, our technique and our mastery of what we are playing.
As a piano teacher I have seen how much students can learn from making mistakes. For instance, it is through mistakes (and questioning too) that students can learn to differentiate between the notes, whether it is on the page or on the piano or keyboard. If you were say playing a piece of music that you kept on playing an F, when the note should be a G, the more times it is corrected by a piano teacher or even yourself, the more it sticks in the brain that the correct note is actually a G and not only will that piece of information help you play that piece of music accurately, but it will also help you get the G right in other pieces, as you are now less likely to miss read it or miss play it.
Making mistakes in your timing can be a way of getting your timing accurate, especially for those that find having accurate timing a difficult thing to master, like I did. I have several memories of getting my timing wrong when I was a piano student and my piano teacher forcing me to drill certain tricky sections of the music so I could learn to play the piece correctly. At the time I did not appreciate or enjoy doing this, but these drills that I had to do not only fixed the piece I was working on, but it gave me the chance to really be able to play certain common rhythms AND a way of knowing how to fix my timing, should I ever come across a new and challenging rhythm. This not only helped me when I was a piano student, it helps me even today both as a piano teacher and as someone who likes to play challenging pieces on the piano.
Mistakes are also good for understanding optimal technique. A classic example is when a student is learning to play staccato, which is playing the note very short with a bounced movement. The majority of piano students go to bounce the note using their elbow joints and keeping their wrists stiff. This is actually not the ideal as the wrists need to be nice and loose, as this is really where the bounce on the notes should be generated from. If students don’t actually make this mistake and then have that mistake explained, they may never understand how important a loose wrist is, not only for producing the correct effect, but for preventing stiffness or injury to their wrists.
There are just so many examples that I can think of, where making mistakes not only corrects in that particular instance but it gives the person a greater knowledge and skill to be able to apply to future pieces of music that they learn.
As far as I’m concerned, mistakes are not to be avoided at all costs, they are simply a learning tool and they are certainly not anything that someone should be disappointed with or get frustrated over. I think that the ideal attitude towards mistakes is that they can be a fantastic learning tool as long as you have the attitude of being willing to learn from your mistakes.