A lot of that will vary by specialty, type of practice, and what you're looking for in a program. Off the top of my head I came up with these. I think I either asked or was able to find answers beforehand for all of these things when I was applying.
Are there on call duties, how frequent are you on call, how often is a resident called in, is there extra pay for call-ins
What does a 'normal' day look like (in particular how many hours a day are residents at work)
Is there a formal review of your performance
Are there institutional requirements of the program that are outside of the specialty college requirements (e.g. my program requires three publications for completion but ACVP does not require any to be board eligible/a diplomate)
Does the salary cover cost of living in the area
What are research interests of faculty
What is the a average case load of the specialty and how does that compare to other programs
How many technical staff are available for your service
Do you get to/have to rotate through other services
Are courses and/or a graduate degree required/optional/etc
Is there teaching and what is the nature of it (e.g. students on rotations, formal lecture)
Is there sufficient time for meetings, networking, etc
Edit: Boards pass rate
...I could keep going but you get the point. To the best of your ability, you need to know what you're getting yourself into.