Hmmm...interesting question. I'm trying to think what I would want to ask someone if I were looking for a new spiritual director.
I think part of the question is why you are seeking spiritual direction. If you are discerning a vocation then you would want to ask questions related to that and those questions would be different from someone trying to deepen his/her prayer life. I'm afraid my reason for wanting a director is more general -- I want to be a better disciple and have a deeper relationship with the Lord -- so it's hard to say what questions might clarify whether someone is right for me or not.
If you have a particular spirituality you might want to ask about that. Though I have to say that it's not something that applies to my director. I'm a Benedictine Oblate and he has no relationship to the Benedictines. When something comes up related to this -- "well, in the Rule St. Benedict says blah, blah, blah" -- he'll just ask me to explain or clarify anything he doesn't understand. So he wouldn't interpret the Rule for me but he helps me figure out any issues I may have with it.
I can think of qualities I would be looking for in a director but I'm not sure how to interview for them. I want someone who is holy and wise, someone who is clear that this is my relationship with God not his/hers (in other words, help me on my journey, don't try to turn me into a clone of yourself), someone who knows when I need support and when I need to be challenged, someone who seems to understand what I am trying to say even when I'm not totally clear about it myself, and just in general someone who can help me see where the Holy Spirit is working in my life.
This is rambling and probably doesn't help. I hope you find a wonderful director. Mine has been the greatest gift in my life!