Any ideas the best way to locate and vet a good teacher? I know plenty, but I have no idea if they are any good or not. I guess I would need to be a teacher myself to tell!
I have the same dilemma. Certainly here [Beds] there's not much imagination w.r.t piano teachers - "Piano teacher ABRSM, all ages' is about all you'll get w.r.t advertising and not much in the way of web pages where they explain their teaching.
Word of mouth perhaps - but the only people I know who play their words put me off their teachers or they live miles away.
Other than that, it's a case of ringing / speaking to them all, and perhaps having an interview / sample lesson with a few.
Bernhard claims the teacher appears when you're ready or something similar - and that inexperienced teachers aren't a bad thing for inexperienced players, you still learn something - on the other hand he also teaches absolute beginners and gives very appealing numbers for the length of time they take to learn - if you're 37 [or even if you're not] it's self evident which sounds better

But, you're evidently intelligent enough to read through the posts here and decide whether Bernhard or Hanon or someone else is onto something, so I suspect you'll be able to fathom out whether a teacher is telling you what you want to learn.
At least that's my rationalisation of what Bernhard says above - I'll get a better teacher now than I would before reading this group both because I think I know what I want from them, but also because I know what to take with me [a realistic plan of what pieces I want to learn, what exams I do / don't want to do etc etc - all of which is discussed in here] as well as having a better idea of how much of a buffoon I am on other things. It's a cliche, but knowing what you don't know is more helpful than "not even wrong"
So my criteria, FWIW, not well-informed, biased and prejudiced is :-
(a) Practise I don't care about too much about - unless I get a teacher that wants to teach daily - and I doubt I will - then I can use the practise methods that are in here, or the teachers and see what works best for me.
(b) Technique on the other hand is what I want to learn - all this stuff that is contained in the phrase "it's easier to demonstrate than to write down" because I've struggled with Fink's, Bernstein's, Bernhard's and Richard's descriptions - perhaps because it's the co-ordination that's the key rather than the individual positions or movements - as well as the more obvious fact that you need someone to say "Yes / No". They've all helped [if nothing else, they are all the same in many fundamental ways that I think I know what I want to hear from a teacher]
(c) Avoiding giving too much away and having the teacher tell me what I want to hear - because the chances are they'll know about all of these methods and techniques - whether they know how to teach it or whether think it's right or not - I want them to tell me how they teach and not say "Yes" - and I'm sure they don't want to hear "I read on the internet..."
(d) Avoiding people that teach total beginners who are kids on the whole. They need at least one adult student who they can show is being taught proper technique from day one and that they are teaching that adult in the belief that the adult is learning the piano [not making up the numbers or getting therapy from it]
Apart from that, the plan is sit down, play something and let them say what's wrong, what they'll do to fix it [they might have their own ideas anyway, it's not like there aren't equiv "What should I tell students" threads here]
There are a couple of existing threads with lists of questions, but unless the teacher is really struggling to communicate, I don't think a formal list of generic questions to ask is going to help that much - it might help with stuff that didn't occur.