Having recently graduated dental school, here are some questions I may have asked (aka things that I found some issue with during dental school and would have liked more of a heads up on). These may not be appropriate given your interviewer's area of expertise (if they're didactic clinical faculty, they probably don't know about the struggles of scheduling patients in clinic). Or maybe you'll think these come off as too jaded. You'll likely want the answers to these, but of course find the appropriate person to ask.
Do students have their own chairs in clinic? (If you already know the answer is yes, don't ask, if you know it's no then ask how difficult it can be to obtain a chair, who is it shared with, or is it a free for all.) How many patients are you expected to see daily/weekly in clinic, and what's the average. Is your encounter rate with patients tracked and if so, what do they do with that information?
What kind of patients are seen in the clinic? Are they mainly medicaid, self pay, a mixture, or other? If it's insurance based, do students have difficulty finding patients who want to pursue tx not covered by medicaid? What does medicaid cover in this state? (This boils down to my experience where posterior crowns were not covered, so I did not get to do as many as I would have liked because pt's didn't want to pay out of pocket) This is really a broader way of asking How much experience do students get in crowns? Bridgework? Implant restoration? Endo?
And the biggest most important question of all that you probably won't get a super straight answer to is "Do students have difficulty meeting their requirements? Do they graduate on time, and receive their diplomas at graduation?" Hell, you could even ask what happens if you get held back for that one last endo you couldn't find. Does it keep you from starting your residency on time?
You should also probably ask about social stuff like whether people live at home or are closer by and want to socialize, how much do students hang out outside of class/resume building extracurriculars- but that's probably better off with the students.