In general, it's better to ask staff about the long-term aspects of a program, maybe future directions, other people they're looking at hiring (or who may be leaving), things like that. Stick with talking to the residents to understand aspects about daily life; the rotations, supervision, call, benefits, all that.
Another aspect to look at with staff is the approach to fellowships. Some programs like to take their own residents. Many, on the other hand, prefer to have their residents go elsewhere for fellowship, and they prefer to bring in someone from outside for their own fellowships. It gives the fellows a broader view, and more different viewpoints to look at a disease, and many feel that it's a better way to train. If you think you know you want to do a fellowship at a certain program, you want to make sure you know ahead of time if they like to take their own residents, or if they like to take them from elsewhere.
Overall, the questions aren't tremendously important. I can't think of any time that we've said that we have to take someone or that we won't take someone based on questions they asked in the interview. You want to ask enough to show that you have interest in the program.
The programs are also trying to sell themselves (even though it doesn't feel that way when you're on the interview side), and they want to make sure they get qualified residents who will work hard and get along with people there. To get the best fit, they want to make sure you have a clear picture of what the residency is about.
Dave