Asuming he's doctrinally sound, you want to see if he's spiritually sound. So ask for a recent example of something in his life he's repented of. How he answers (and how he reacts to having to field such a question) may tell you a lot about his heart, his life with God, and his confidence in the blood of Christ as his sole source of approval.
I'll disagree with my brother below and very much agree with this statement. This type of maturity and soundness isn't taken as seriously as it should be. To be sure it's easier to ascertain a minister's knowledge of Scripture and theological soundness, which, of course, is very important. But, you're looking for a reaction and/or attitude as much as anything here. If he has trouble thinking of an answer it might be b/c he's not practiced in the discipline of repentance. And then he's just one of those egg-head, Pharisaical Christians who'll be at a loss when someone needs a genuine pastor.
I agree with Ben. This is not a type of question to ask in the context of complete strangers. How would you respond if he answered "that's a good question. What would be the area of your life that is most unbiblical? Where would I find my greatest challenge pastoring you?"
I see what you're saying. But, shouldn't we know something about the man we're going to call as our spiritual leader and teacher? We're not speaking of hiring a kid to bus tables, or even a CEO of a fortune 500 company. We're talking about the leader of a Church of Jesus Christ. I don't recall our Savior being shy about discussing the important issues of life (e.g. the Woman at the Well).
Also, how can we properly discover whether a man fulfills the requirements of Timothy and Titus unless we know something of the man personally? You'll notice from the list of requirements in those epistles the descriptive adjectives have much more concern with piety and lifestyle than with ones doctrinal soundness (although both are important).
Also, I think it's important to be honest with ones pastor regarding your weaknesses. How else will he know how to pray for you and teach you?