I think the one reasonable expectation of all coaches/trainers/instructors is that they not lie.
Beyond that, what you look for should vary depending on goals and location. If you want to be a top international competitor, you need to relocate to where the top international competitors are, and ride with them so you can learn.
My trainer will eventually retire (right now he says in about 10 years, so I have a lot of time to figure it out if he keeps riding that long - into his mid-60s), so to some extent I think about what I will want in my long in the future next trainer.
Hopefully by then I will have made more than one GP horse myself. I won’t theoretically need someone to ride for me so much, but will likely always have straightness problems because of nerve damage. I literally can’t feel my left seatbone, and so I will need to ride with someone who is VERY good at seeing and pointing out crookedness. I can quickly get out of whack. By then, that may mean riding with a friend who has worked up the levels regularly rather than going to a new trainer, we’ll see. But regular eyes on me to counter the crookedness will always be important. At that time, I may be happy just taking regular clinic rides with trainers who come to the area - as our community seems to be growing, I don’t see why they would be fewer later than there are now, but that can always happen of course.
If it were as things are right now, I would want a trainer who can ride my horses, who does not insist on the low and overbent garbage, and has trained a horse him or herself through FEI. However, showing isn’t a high priority to me - so if that trainer has trained the GP skills (verifiably) on a horse who can’t get through a GP test, that’s ok to me. That’s the case with my trainer, whose stallion may end up a GP horse, but has had multiple turnout injuries affecting his ability to develop the stamina to make it through a GP test. He’s far exceeded the expectations around him from when he was young, with less than ideal conformation and energy level (he’s VERY mellow), and scores have gone up with training. I’m interested in the training and development, more than showing, so seeing that my trainer was able to so improve a horse is a huge plus to me.
We actually have multiple trainers who have trained horses up the levels in our general area - more if you include Phoenix area as well. There are also some who have shown horses others trained. The development of horses is the part I care about, but if a trainer got the actual GP scores on a borrowed horse but also has trained horses up the levels, I wouldn’t think less of that trainer. (And in fact one of my favorites had that exact situation.)
So basically, it just depends. We all have different situations and want different things.