If something the teacher demands seems to contradict psychology or biomechanics, cross him off your list. As I said, the teacher should provide all the relevant explanations during the lesson, but if someone has questions after the lesson, he has to be able to answer them exhaustively and logically. In watching the teacher ride, you should immediately notice the quiet, elegant, supple, balanced, effective seat. A rider with a poor seat is a poor rider. Somebody who cannot sit the trot, or whose legs and hands seem to be bouncing all over the place is a novice and should never be a teacher at this stage of his own development.
Teachers can only teach what they know.
Under the best of circumstances you will end up riding like your teacher. Therefore, ask yourself if you would be proud or ashamed of yourself, if you rode like the potential teacher candidate. Another test is to ask yourself whether the candidate you are looking at stands out among a crowd of riders as a professional in a positive sense. There was nothing in their riding, their posture, their demeanor, their turnout, that suggested that they were competent enough to teach a horse or a student anything. On the other hand, when you look at my own teachers, they stand out among a thousand riders, due to their exquisite elegance and quiet effectiveness.