I was the "fit" interviewer at several companies and my primary goal was to assess how well the candidate would "fit" in the organization. I firmly believe that this is the most important thing to get right. I might be able to teach you, say, c++ but I probably can't teach you not to be a horse's backside or a know-it-all or a person who doesn't take criticism well.
I'm not sure there are 'magic' questions you can ask to get the answer. I could ask "tell me about a time you had to deal with a difficult problem" or "if you had to deal with a difficult co-worker, how would you do id?" but I'd likely get monkey-business, canned responses from the candidate much of the time.
Instead, I'd get them to talk. The goal is, I think, to shut up and let the candidate talk. My boss would often sit in the interview and blabber on about this and that - a big mistake in my book - and the candidate could just be polite and they'd like them. I tend to get them to talk about things on the resume, things they mentioned in response to questions, and perhaps talk about the work environment they have been in.
Example - if I wanted to see how they interacted with others, I'd ask them to describe the team environment (working conditions, desk space, were you in cubes or separate offices or just desks in a room. What did they like/dislike about those arrangements. I don't really care about the specifics of where they worked - I'm not going to be interviewing at their place - I'm really wanting them to get out of the 'interview mode' they are surely in where everything is formal and the shirt is pressed and the candidate is wearing a mask. If I can get them to forget that they are trying to get a job at my place and just be open, by getting them to chit-chat with me rather than tell me the answer to "where do you see yourself in X years", I think I can figure them out pretty well.
I think it takes certain type of person to be the 'fit' interviewer - I'm a reasonably good one because I'll let them talk but I don't come across as the stiff, formal company guy. At the end of the interview, if I haven't been able to get them to 'be real' for me, then I have to think long and hard about the candidate. I might even call them back for a second interview to ask some more questions, but I'm really looking to see how their personality is. Sure, I'm interested in if they have a background in some technology, but the goal of the 'fit' interviewer is to assess, in my opinion, whether the candidate is the kind of person I can trust and work with 40+ hours a week.
I'll also ask lots of questions of his references to get them to open up about him. This is hit-or-miss, but at least I'll try.
Just my two cents.