One of my favourite interview questions was: What is your philosophy of worship? It's a huge question but can also give huge insight into what will drive a person in their ministry and the choices they make for your church.
Another one that stood out was "describe a 'mountaintop' experience you have had in leading worship?" (referring to Moses meeting God on the mountain).
I'm thinking above and beyond the standard - "how do you deal with conflict?" types of questions.
For what not to ask - avoid making someone worship plan on the spot. I've had someone ask before, "what song would you choose for a sermon about holiness?" All you're going to get is the low-hanging fruit because you have a person in a stressful situation and feeling a time crunch of not wanting to make the interviewers wait, plus I think it discounts the creative process and assumes that solid worship planning can happen on the spot. Now, a way to phrase that question that could get a more thoughtful response would be, "what is a song you love that talks about the holiness of God, and what about it speaks to you?"