Qualities a guitar teacher needs to have:
Patience. You need patience to sit through lessons with struggling students while keeping a positive attitude.
Motivation. You really need to be motivated about teaching. A lot of guitar teachers aren't motivated about teaching but see it as a way to earn money with their guitar skills.
Communication. This is a skill every teacher should possess regardless of what he is teaching.
Teaching ability. Not everyone makes a good teacher. Some people are skilled in their profession but make bad teachers for whatever reasons. Teaching is after all a skill in itself.
Playing ability. You need a certain level of mastery with the instrument.
As for things a guitar teacher should not have, I would say the exact opposite. This would be a teacher who is bored during the lesson. Isn't motivated to get his student to learn, cannot communication whit his student properly, etc.
These insights were given to me by a former guitar teacher of mine, Micheal Murray.