Ask them to talk you through a typical band class for them. Everything from bell to bell.
Don't ask their greatest strength, but DO ask their greatest weakness. I think this gives you insight into whether or not they are introspective and smart enough to at least know what they dont know. Follow up with: how do you plan to address those deficiencies in your teaching?
What do you envision your role being on staff? Tell me how you deal with someone critiquing your methods?
Just my thoughts. GOod luck.