I've gleaned over what everyone has posted, and while I would love to toot my own program, I wanted to give a few pointers which have guided me to set up my office the way I have.
1) Access and role of prehealth advisor or committee. If you don't find at least a website about health professions advising, you can infer how important advising premeds really is at a school (and sometimes you'd guess wrong but in an era that everyone has a website...). The other threads talk about how important it is to have a committee letter, but it's also important to know how active the prehealth advisor and committee is to keeping students informed throughout an undergraduate or postbaccalaureate education.
Rules of thumb: Stay away from asking for percentage of people who got into medical school; the answer I give is much more complicated (do you mean allopathic, osteopathic, dental, postbac, high-achievers, ... ?) even though I do provide some data on my website. Pet peeve: please do not ask me about "how to switch from biology to premed" as a major. Most advisors who do have websites expect you to have read and understood the entire website, and I clearly will not schedule appointments with anyone who says, "I want to talk about something with you" if it's clear the person had not checked the website. (Sure, I could use a lot of reorganization, but in the end, you are responsible for the knowledge, and I can't help you learn how to tie your shoes if I gave you instruction on that.)
2) Volunteering and clinical opportunities, especially in rural or urban areas in the US or perhaps opportunities abroad. I cannot emphasize how important this is to an application. It's always easy for some students to choose a school that's got a hospital right next door. Then the challenge is to see how much initiative you have to go beyond the convenience of your doorstep. For students at smaller liberal arts schools, there aren't as many convenient opportunities, so you have to learn to make opportunities for yourself. And to me, that scores points for perseverance, planning, and diligence. But an awareness of and education about the health and societal needs of the underserved will broaden your vision to how much health care is sorely needed.
Unlike many other programs, I don't organize a volunteering or shadowing program (though I advertise the contact information). I'm close enough to DC that there are plenty of opportunities, and I would rather my students choose what they want to do for themselves. You're adults, and I'd need to be paid more and have an extra 20 hours added to a day to get that done right.
3) Support networks. How active is the premed club, predental club, and so on? What are their service opportunities that they're proud of? Who do they advertise as recruiters coming to their campuses? Do they have connections to students who got in and those who did not (but might reapply)?
4) Research opportunities... sort of. You need connections, and research is one great way to get connected to cutting-edge breakthroughs that could guide your practice in the future. But social science research/clinical research is also very valuable. Don't hesitate to get your feet wet in the difficulties of doing human subjects research.
And for the record, I went to Duke as a premed, and I think I turned out pretty well. 🙂