I think its quite tricky, but there's a few things I'd be looking at.
I'd not judge on age, or not age alone. Its good or bad depending on other factors.
An older doctor who keeps up with current medical practice and research is probably going to be very good. A few people are like that.
I've noticed young doctors in hospitals tend to speak with utter confidence in themselves, in a way which old ones don't quite seem to. And they have been totally wrong. I had the impression they have not yet had time to see how real life is different to books. Unfortunately it easy to fall into the trap of judging someone by the confidence with which they speak. Most of those young doctors will eventually turn into those old doctors who don't keep up.
I try to evaluate what kind of person they are.
Nina, you mentioned discouraging vitamin supplements, but taken too far that could be bad rather than good. One reason people take them is because they can't discipline themselves to eat properly. All the time I've been very overweight no doctor ever managed to get me to eat properly. I knew how, I just couldn't change.
I take notes and double check everything they say or recommend to see if its sensible. I may not know enough to treat myself, but I can have a good go a checking on what they say (prescribing premarin in the last decade for example, that was really bad). If I get a chance I try to ask the same questions from different doctors, and ask questions to which I already know the answer. Questions I don't even care about, but which I can use to evaluate them. I try to see if they are up to date. I've asked doctor about other doctors.
Perhaps ask about WPATH and see if they know about it, if anything. See how flexible they are about it (I don't much care for it myself). I asked my psych early on what he thought about WPATH and DSM and got a very shallow answer (and I like/respect him).
I like a doctor who's going to take my requests seriously, and if he thinks I want something I shouldn't be prepared to explain why or argue the point. I'm not interested in their moral objections over mine, or them thinking I can't be trusted to be responsible. I want a doctor open enough that I can work him out - it makes me worried if I can't read them.
I collect all the little bits together over time to get a better picture, assuming it lasts that long.
The bigger problem with Endo's with transgender experience is that there's not many around and not a lot of choice. Lucky I got a good one, or at least I think so.
I think I sound a bit crazy, but its a piece of how I view things generally.