Hi, Totoro- I'm sure you know that my search has been a struggle (and that's an understatement). LOL! But, a few of the more basic things are hours of appts. (if scheduling is an issue), will they be accessible by phone between appts., do they do CBT on a child this age (important question- don't be surprised if instead of saying that they don't, they say well, we normally don't try that or find it not effective on young children -we find behavior modification works better), what age group of kids do they normally work with, what diagnosis do most of those kids have (some have most of their experience with adhd), what kinds of things can they do to help with XXX (in your case, social skills), do they have experience with mood disorders (big one), but the most important thing- meet them in person if you can and see if you are comfortable with them and if you think they'd interact with your child well.
With me, one of difficult child's big issues was having a male, so that eliminated a lot of prospects. then, all the profs. who ever evaluation'd him felt that he needed help with problem-solving and coping skills and that this was a big problem for him and what was leading him to be self-destructive, and I had found that The Explosive Child techniques worked well, so I did want someone who thought along the lines of helping difficult child learn by teaching him to think through things by actually helping him step-by-step, rather than by concentrating on rewards and punishments all the time. But, this could be different for different people- depending on the issue. Since I found a method that worked well for difficult child, it would bother me if a counselor had not even heard of it. So, if there is something you know works well or doesn't work at all, you might want to ask about that, too.
One of the biggest things I see- and this is just my opinion- is that there appears to be one concept (the predominant one) that medications take care of the "mood" issues and behavior contracts (rewards and punishments)- which is "behavior modifcation therapy" will teach the child they they have to conform to the world's rules anyway. Then, there is another concept (more modern and less predominant) that medications don't take care of all mood issues and that there is a different way to teach the child to live by the world's rules. Usually, a counselor will not bring either of these concepts up and will just automatically start providing whatever they are used to doing. If the parent is aware of this, the parent can decide which approach they want to seek out. Tdocs aren't always used to parents asking questions like that. But, if you choose one approach, it is good to ask about which approach the counselor is going to use- and make sure you're in agreement about their attitude toward mood cycling to begin with. That's just my opinion- others will not share it.
These are just my 2 cents- again- I can't say it has helped us land the perfect therapist... Good luck!!