Well Ian....since you mentioned it...I was going to steer clear of this, but...I've encountered quite a number of absolutely horrendous teachers. If you see a sign that says "Lessons..accordion, bass, trumpet, piano, sax, guitar..etc." Run like hell. NEVER, NEVER pay for more than one lesson at a time when you're just starting with someone. Use your noggin and see whether your new teacher has a clue about the kind of music you want to go into. If the vibe isn't there at the beginning, it won't be later. Don't be afraid to say you're not comfortable if you're not. I've had four women come to me in the last couple of years because another instructor hit on them...during the FIRST lesson yet!
The easiest (for me) person to work with is someone who's been playing for a couple of years and knows what direction they want to go in, or a veteran player with good habits who wants to learn some flashier stuff or tricks to make things easier. The hardest is someone who has played for many years but because of some flaw (that's become really ingrained) feels they haven't improved for a long time. In that case you almost have to go right back to the beginning, and that came be emotionally difficult for both player and instructor.
One of the things I do that is radical but I've found to be very useful (after the initial shock) is to ask folks who come earlier to sit in on someone else's session. It kind of demystifies the process and after all, I want people to get to the point where they don't worry about making mistakes in front of others. Doesn't work for everyone though, so I don't push it. It hasn't been uncommon to have someone who came for a 7 oclock session still there at midnight. Some sessions have turned into impromtu jams...and that's where you REALLY learn.
My feeling is that EVERYONE can learn, even if comes down to another instrument than the one they started on. I mentioned earlier about a few folks that I just couldn't help no matter how hard I tried...but that was a few years ago and I've learned a lot since then. Wish I could try again with them.
Rick