A lot of people when they start out assume that if a person is teaching Martial Arts they must be an expert. Or just because a person is an excellent Martial Artist, that they will also be a good coach. Unfortunately it's just not true. They aren't bad per se, since they aren't doing anything harmful like hurting their students or anything otherwise dangerous. They just aren't very good at their job.
The Cardio Coach - This is a really popular type of coach in a lot of competition schools. While Cardio is really an essential part of training, if that's all there was, then Crossfit guys would be UFC champs and Olympians in Martial Arts. Unfortunately, there are instructors out there who think that the metric for success in martial arts is how tired they make their students.
The Pads Guy - Pads drills can be a really useful development tool. But there are some coaches who would have you spend almost all your time hitting pads because they don't actually know that much. You see this a fairly decent amount of modern Boxing and MMA gyms where the coach will just have you hit combos on pads but then those fighters can't translate those skills in the ring.
The Make Things Up Instructor - These guys are the worst. You see this a lot in schools that try to offer martial arts cross training in arts they haven't actually studied. A lot of these Instructors feel like they have to have all the answers, so when you ask them something they don't know, they make up an answer. Sometimes they will just make up a BS technique and sometimes they will give you some ley line Woo woo, chi BS, but it's all pretty much equally wrong.
The Repetition Teachers - These instructors believe in repping for numbers sake. The truth is that while doing a technique a thousand times will make you better at it, it doesn't occur if you do it the same way each of the thousand reps so your development becomes stagnant. They teach this because they don't actually know anything else.
The Aggression Wins Instructor - These guys believe the answer to everything is just more aggression. You see this a lot in styles like Krav Maga or other "street lethal" arts where they just have different versions of grabbing hold of someone and throwing the same elbow or knee 5 times in a row while yelling . This shows a very limited scope of knowledge by the instructor.
So what should you be looking for in a good Martial Arts Instructor?
A good martial arts instructor should understand not only the techniques, but the principles at play and the systems they are part of. They should have an honest and deep working knowledge of the art they are teaching and not exceed the boundaries of them. If they don't know something, they should be honest and not insecure about the limits to their knowledge, but willing to find out. They should have a clear understanding of effective training methodologies that will allow you to develop quickly. They should NOT try to keep you from exceeding them, but instead if they are a good instructor should deeply hope for you to go further than they were able to using their knowledge as a springboard toward quicker development.