How integrated are the 2 degrees? Does the school have programs like MSTP Grand Rounds? Are there opportunities to get clinical experience during grad school?
What are the coursework requirements? Are there MSTP-specific classes? Do you have to take grad classes during M1? How many grad classes do you have to take during your first year in the lab? Do they lighten your schedule with things like shortened anatomy time?
What is the average grad time and what is the range? I've went to 1 school where they claimed the average was 7.5, but I kept meeting LOTS of people on the 9-year plan. hmmmm. Talk to students; don't just rely on the director's claims.
What are the research strengths? Is there good variety within your department of interest?
Where exactly is the school located and how accessible is it? This is particularly important if you want an urban location. For example, in terms of location, Cornell =/= Columbia =/= Einstein, even though all are in New York City.
Housing. Do MSTPs get studios or suites right off the bat, or do they have to live in dorms for a couple of years? Is there on campus housing at all?
How big is the class size? Do you want 3 peers or 20? If you're a bigger presence on campus, you tend to have a bigger say on how policies affect you as a group.
Is there good advising and support to make sure you don't flounder, especially during the PhD?
All of the questions wou'd normally have about a med school, such as curriculum, grading, exam schedule, class size, facilities, social environment, diversity, non-academic opportunities, etc.
To be honest, I didn't realize I should think about most of these things until I started interviewing. You want to know how I chose my schools? I wrote down the cities I could see myself living in for 8 years, and then I applied to all of the schools in each city, and then threw in a few extra. Some people, on the other hand, apply to the best schools by ranking and research area... but I find location to be a VERY important factor, so that was my least common denominator.