I interviewed at 8 med schools and 18 residencies (about 85 interviews total). I asked at almost every single one of those interviews about the weaknesses of schools/programs were and what they were doing to improve. I had very candid and substantive conversations probably about 90% of the time. It was most likely the single best conversation piece. This was three fold.
First, schools/programs love to talk about things they are building/improving. If they don't have some pet project to tout, they will talk about the structure that they have in place to field student concerns and address them. I remember one ad com member for medical school said, "Honestly, I don't think there are any weaknesses/problems right now, but in the last 5 years we dealt with X, Y, Z and countered them with A, B, C."
Second, assuming you are a decent/good applicant, you are picking your school/program as much as you are being picked. You can ask this question without coming across as entitled, it isn't terribly difficult. It is the most direct way to get good information on what people think of the place that they are at. From chairmen of departments to professors to current med students/residents, they will be able to offer you a window into their world which is invaluable.
Third, the goal of any interview should be to show off your ability to have a reasonable, substantive conversation. Asking about someone's research when you have no connection to it and no real interest in it is brown nosing at best and much harder to pull off than having a conversation about something that is of interest to both you and the person interviewing you.