In an absolutely fascinating opinion article, Adam Grant opined that "those who can do, can't teach." I laughed as soon as I saw the title. It was pretty clear to me where he was going. Grant argues rightly that the greatest experts in a subject are not necessarily the best teachers. My usual way of getting to this issue is to tell an entry-level person that the best coach will never be more than two levels above you. Beyond that, the expert will be highly abstract, assume the unassumable about you, and won't be able to put the skills in a concrete package.
But Grant's way of going at the issue is so very useful, it needs to be added to your toolkit for coach selection.
First, pay attention to how long since the teacher studied the material. Ignore the top universities' boast about how most of their classes are taught by top faculty. The best teachers are probably grad students who just learned the material and know what it's like to be a beginner. In my post-doc work, I signed up for a course in adult learning and was initially disappointed that it was going to be taught by a teaching assistant, a grad student in his last year of PhD. From the start, he surprised me with his thoroughness. Later in the semester the top prof in the field subbed for his grad student when he had a bad case of the flu. Wow, was I glad the TA was teaching. The expert couldn't get the cookies on the bottom shelf for us no matter how many questions we asked...
Second, learn from overachievers. The people who accomplish the most with the least natural talent and opportunity. When I was just 18-years-old, I worked in a Detroit factory in "general lap"--the "parts" finishing group. After I'd been there a few months, the foreman assigned me to a complex finishing job and rattled off the task. I played around with it for half-an hour, making no sense of it, until a leader in the group saw. He had sailor's language, was rough looking and acting as though he didn't understand anything. Seeing that I was having difficulty, he told me he'd show me how to do it. He did two of the small pieces, then said he needed to watch me. I tried a couple more and he stopped, saying "hold your metal sandpaper this way." One of the little pieces--a bushing--flew off the lathe. And he chuckled with me, showing me once more how to use my left hand differently than my right hand. In less than hour I was knocking out the required number pieces with ease. Obviously, I never forgot that experience. Simple guy, very close to the basics, never could become a foreman, showed me how to do things the well-educated foreman couldn't explain.
Third, focus on how well the teacher can communicate the material as well as how well the teacher knows the material. Communicating is especially hard for experts teaching basic classes. Fewer and fewer people can converse well today. The truth of the matter is that unless the person can actually use your language to explain, you're going to have a great deal of difficulty learning. I took a freshman logic class from a full professor my first year of college. I had a great deal of difficulty even though I was one of the few who kept asking questions. What frustrated me was that he never could seem to answer the questions I asked. And like a lot of students in the class, I did poorly and stayed away from philosophy until I knew the prof knew his subject and could really communicate well.
Grant's conclusion clarifies the whole business for us: Being a great physicist doesn't make you a great physics teacher. You don't want to take your first physics class with Einstein. You want to learn from his protege who has spent years figuring out how to explain what it would be like to chase a beam of light.