Three essential elements of good piano technique that are sometimes neglected by both teachers and students are breathing, listening, and (surprisingly) moving.
Breathing
Like any athletic exercise, a pianist’s mental and physical facilities are enhanced by breathing normally. To the extent possible, it’s useful to stay mindful enough of your breathing to notice any tendencies to hold it.
A useful trick for making sure that you breathe normally and evenly is to mark spots for breathing into a piece, much like singers do. This can be particularly helpful in emotionally intense places in the music, when holding your breath would be akin to restraining your emotional expression.
If your breathing is consistently shallow, consider supplementary yoga or other breathing exercises. You may also want to correct “mapping errors” in your breathing, which you can learn about in the excellent book What Every Pianist Needs to Know about the Body by Thomas Mark, one of my teachers.
Listening
Active listening is one of the most important factors in good technique. Your ears can tell you a lot about the quality of your technique. Chances are that you will sound good if you’re playing with good technique, and not so good with poor technique. Always listen as you play!
Moving
The music you make depends on the movements you make. If you want a different musical result, you must move differently.
Music itself is movement. You should always be in motion, even when holding a note. I like how Taubman teacher Edna Golandsky puts it: The moment the arm stops moving, the music stops moving.