Apart from the cursory and obligatory "experience" questions offered here and generally asked (how many dives, last dive, etc.) I think the behavioral (sp?) questions are more important.
Case in point: Once, I hooked up with someone who, when asked these most basic questions, came up stellar: Dives a lot, dove recently, dives in my neck of the woods (read: not a lot of recent resort diving...) so I thought it was going to be cool.
After a couple of dives, this guy fell into the "hunter / gatherer" camp. I've done this so many times, I've basically got it down to four types:
1) Touring (I'm this type) - get wet, have a look around, get out.
2) Hunter / Gatherer - lobster and spear fishing are number one, good buddy skills are, well, not number one.
3) Photographer - stopping and shooting, with maybe a little diving mixed in.
4) Newbie.
Number 2 is the scariest one for me. In So Cal, these weekend warriors are everywhere, disguised as divers. They talk the game, but once in the water, its every man for himself. It scares the heck out of me. The classic S.O.B. To be avoided at all costs.
You gotta get into the dive objective questions. Are they AOW, are they in a DM program (fast-tracking dives is a hint here...) etc. Do they know how to use their compass? Have they ever missed the dive boat (we all have) and come up someplace else...what'd they do? What's they're typical dive planning process...dive 'til the gas is gone, then come up? I always ask if they are hunters, are the on the trip to hunt, when was the last time they did a buddy drill, have they ever been in an actual OOA, etc.
I NEED this person to stick by me, as I'll stick by them...I want to be paired with a cool head, and if we're not on the same page its time to get someone else. I've been paired up at dinner, and over dessert I've approached the DM asking for someone else. Its your life - you gotta be comfortable with the person.
I have an equipment config that's different from most of the people I dive with (BP/W, Long Hose, etc.) and a supply of safety gear / back up gear (B/U mask, HID light, etc.) so as I go through my gear, where its stowed, how I donate the primary, etc. its an excellent time to get into the behavioral questions.
Its as important for me to know the person as it is to know their diving resume.
Take this stuff very seriously. Its important.
K