What are the lesson horses like?
How nice is the instructor (believe me, this is important, I've had one HORRIBLE instuctor, I quit hunt seat after that)
Does the instuctor yell? Some people don't mind when they yell, some people do, my mom can't stand it when Mrs. Jenny yells, but I don't mind it.
How focused is the instructor on the lesson? Some trainers get SO distracted w/ other things/barn things/talking with friends.
Does your trainer praise you and tell you what you do right, instead of only telling you what you need to work on? Constructive criticism.
Make sure they are nice to the school horses and ask if they get turned out regularly.
Make sure none of the lesson horses are studs.
Does the trainer spend time with each person in the lesson individually?
Does the trainer ever tell you to hit the horses too much or when they don't need it (some trainers can be downright cruel to horses, some, not all)