Diversity is equally if not more important than case numbers. In fact, you should ask about "key indicator" cases. These are the cases that the Academy determines are the most essential cases ENT residents must know how to perform prior to graduation. Deficiencies in these cases often result in (among other things) probation of a program, loss of a resident (or denial of additional resident approvals). These are things like ethmoidectomies, mastoids, thyroids, neck dissections, etc. More important cases.
What program has the better experience - the program with an average of 1500 cases or the program with an average of 2000 cases? What if I told you the former program had residents that averaged 200 sinus surgeries, 200 mastoid/tymp-mastoids, 200 neck dissections, 200 laryngeal cases, 200 pedi neck cases, etc. while the other program had 500 tubes and tonsils, 500 DLs/bronchoscopies/esophagoscopies and residents were counting sinus scopes and laryngeal scopes as procedures? Make sure you know how diverse case load is.
You should look for clinic-OR balance. There are some programs that are all OR and no clinic. This is bad. I've never met a doctor that can efficiently run a clinic without ever having to learn how to manage a load of patients. I've met residents who are excellent surgeons who couldn't work up a patient if the steps were written down on a piece of paper.
Look for diversity of faculty - you want representation from all the subspecialties.
Look for research experience; make sure you look strongly at programs that give you experience doing research.
Look for programs that have regular didactics. This can be grand rounds, M&M, cochlia, resident/attending grand rounds, visiting lecturers, etc.
Look for resident cohesiveness. They don't have to all be lovey-dovey or go to parties together, but if they all get along well, that's a good sign. Hard to gauge while on an interview because everyone behaves well.
Look for new hires. Find out who has left in the last 5 years and why. Who's on the verge of retirement?
Is ENT a division of surgery or a department? Seek the latter program.
How is the hospital system? Is the hospital recently acquired or has it been a stable system?
How about trauma? Is it split among plastics, ENT and oral surgery?
Don't ask about call schedules; it makes you seem lazy. It is what it is.
Don't ask about book allowances and whether you get loupes or not. This is petty when juxtaposed to the educational value of a residency program.
Will the program pay for your trips to meetings if you present? What if you don't present? (Formulate this question to make it sound like you're not asking about the money.)
What is the publication track record of residents?
How are the fellows integrated into the program with the residents (if there are fellows)?
How many residents go into fellowships each year and what fellowships are awarded?
I don't remember what I asked, but if I were able to do it again, I'd ask about what I stated above.
Attendings being jerks or generally being disinterested in me. One attending picked up the wrong folder and started asking me questions about my experience as an Outward Bound instructor (I never was). When I was applying, I got annoyed that attendings hadn't read my application closely, but being an attending now and having reviewed many applications each year, it's tough to keep them all straight or remember every detail.
Look at the department library. Look at the age of the books. Look at the conference room facilities. Pay close attention to the equipment in the clinic -- is it modern? Do they have aged microscopes? Do they lack sinus video equipment? Look for nurses, PAs and medical assistants in clinic. Are they around helping docs or are they no where to be found? Look at the ORs (if you get a chance). Old equipment? New equipment?
What is the age range of the faculty? Are they all old? All young? (Both are less than ideal.)
Probably many.