I could think of several things, but first and foremost a really good pitching coach has to be someone who knows his (or her) elbow from third base. Some of the best ones are, or have been, very good pitchers (and even some catchers who know a lot about pitching and pitchers). A good pitching coach---and I'm speaking of the professional level, because that was my experience---is one who will take what a pitcher is giving him and show that pitcher how to make the most of his/her capabilities. One who will tailor his/her approach to the individual requirements of said pitcher and stay away from the cookie-cutters. Also, the pitching coach does need to be something of a psychologist, because very often a pitcher's difficulties have nothing to do with mechanics or repertoire or fielding one's position but with what's going on between the ears---and often he needs to be a troubleshooter. I had almost four years of experience working with one such, a pitcher who was way ahead of his time, who could also coach and teach, and what I learned from him was nothing short of priceless---he took me in hand, worked with me and helped me all he could, which was a lot (and he taught me how to throw a devastating slider as well). I can only say that if you find such a coach, hang on to him for all he's worth.
Much of what I've said here can apply at lower echelons of the game.
Goddess of the Slider