Well, having had 3 problem dogs now, I must say I've had more than my fair share of experience with dog trainers. Six, to be exact. These range from inexperienced dog obedience trainers to medical doctors licensed to deal with fearful dogs.
Besides all of the "normal" things people encourage when selecting a trainer (how much experience they have with problem dogs, etc.), I have a list that it has taken me 6 years and 3 dogs to come up with.
1) Know yourself. Do you do better with someone identifying everything you're doing wrong? Or someone who will give you some reassurance and identify what you're doing right? I've come to understand that the second is more my personality. I want someone to say to me: "Oooh, that click was perfectly timed, you prevented him from staring at that dog..... etc." I want someone to say to me "your dog is going to end up fine," not "your dog will end up a biter if you don't follow what I've told you to do." While the latter may be true, I ALREADY KNOW THAT. It is why I'm coming to you in the first place. I don't need to become more nervous about that possibility. Believe me, my mind has already gone there.
2) You want your dog trainer/behaviorist to be a problem solver, not a prescription-writer (and I don't mean a medical doctor...I mean someone who prescribes protocol A for behavior X). Don't buy into anyone saying "this is the way to do it, or else". There are TONS of ways to train dogs. Yes, I'm into positive training, but a dog also needs a stick sometimes. As my favorite dog behaviorist person told me "You don't teach a teenager to drive by only telling them what they're doing right." A good dose of "knock it off" has worked wonders with Sagan. I'm a huge fan of clicker training to train new behaviors solidly, but then some other strategies can help. The best advice I got was to stop talking to my dog so much when all the scary stuff happened.....I was "attending" to his behavior too much. You don't need to be afraid you're going to scar your dog permanently. Things can be undone. The problem with a trainer that says "do this or else".... or "only do this because".....is that it causes you (me) to be paranoid. YES, I've used a water bottle with Sagan in the backyard to break his cycle of barking....you know what? It works. Lots of things do. I didn't have any kind of breakthrough with Sagan until I started using multiple approaches. Is he "fixed?" No, but he's a hell of a lot better.
3) Find someone who doesn't feel the need to correct you while you are doing something with your dog. Of course, if something dangerous is about to happen, that's different. I can't stand being in the middle of something and being told to do something differently. I can't focus on you or my dog, and then I end up doing something else wrong. This will be hugely unpopular but...CESAR MILAN does this. He lets people do things, observe, and then provide discussion, ideas, critique. I don't do well with the "No, don't let him do that" business.
4) Regardless of credentials, you need to be comfortable with who you're working. If who you're comfortable with doesn't have as many credentials, it doesn't mean they don't have helpful information to impart. My dog obedience instructor (who is really just starting to train dogs, AFAIK), suggested one of my protocols with Sagan was backfiring, and suggested the water bottle. I needed that jolt out of namby-pamby land to start looking at dog training as a trouble-shooting mission, not just an "apply and hope" method.
Above all else, don't let anyone make you feel bad about what you're doing with your dog. If you're seeking help, you're better than a million other dog owners out there who give up on their dogs. I had someone (ironically a dog trainer who works for one of the dog trainers I went to), tell me I was selfish for wanting to train my own dog instead of letting him go live with someone else while I "cooled off." There are lots of judgmental people out there.