I don't know about impressive questions, but some questions you might want to ask to know if the school will be a good fit for you is:
Student/admin relations - (get a feel for if the admin is pro students or anti students and or organized, have a friend at medschool with an anti-student admin and he says life is miserable)
General school atmosphere - (as you walk around get a feel for the layout and if you like it, especially where the library is, its lighting and how the library and school smells. I know you think smelling the school is funny, but believe me, when you are spending close to 24-7 at the place, you don't want the layout/lighting/smell to be lame, it will make you miserable in the long run. I went to UT and spent almost all of my time in Welch, been out of college for 2 yrs now and when I go visit friends, just walking into Welch gives me shivers and puts me in a down mood because of its smell.)
Schools focus - are they heavy into research and expect everyone attending to research, are they focused more on science or more on clinical? Match up with what is important to you
Board scores - ask % passing, and their average scores last year (how well they stacked up against other schools)
Specialization - if this is important to you, what % of their classes usually matches (matches is important here) in their residency programs.
What their ideal student is (application purposes) no harm in asking, and if you get a straight answer, you can position your application/statement to be exactly what they want (ask the Dean of Admin this one(
Student environment- ask the students how they like it, is their class competative and cut throat or collaborative, and ask yourself which environment you would do better in. Also ask them why they picked the school, and if now they are there they would have done anything different, and if there is anything they don't like about the school.
Location - more of an observation- how accessible is it to housing, could you tolerate the area of town it is in.
These are just some off the top of my head