I hate to rock the boat, but I feel that the most important thing over all is board scores, because it is any easy place to start and a standard way to compare people, but kind of a ridiculous yard stick for various reasons. I think the next most important thing is letters (if you have good ones). I think the names on the letters are a big deal sometimes. They can help a ton, if only to get conversations started. If you dont have recognizable names I hope it is a non-factor rather than a negative.
I think after that comes research but essentially that is a box that is either checked or unchecked. The exception to that is if you have meaningful research. By this I mean, first author in legit journal, mutliple pubs in a single focus, worked with big names, PhD, that kind of stuff. In that situation I think you get 2 checks in that box and maybe they even try to evaluate it. I think the point is just that you are committed and you can prove it. I think that grades AOA and class rank are all kind of on that check box level because how could you compare a kid from WashU or Hopkins or Harvard with 0-2 honors vs a kid from St. Francis FL Tech Medical College with all honors and Pres of his class of 22. I am not saying the pedigreed applicant is smarter or better, I am just saying there is no way to tell because grades don't have a uniform value. From personal experience, I have many Hs from the pre-clinical years but almost none during clinicals. No one has ever asked me about that and in fact I have received only glowing praise for my academic record. And this happened even at the "good places." So with all of these things (grades, research, AOA, rank, school) I think no single factor is very important, but the more checked boxes you have, the more consistently good you look.
Once you get those boxes sorted out, its the board scores and the names on your letters, obviously the content of the letters is important, but you multiply the content of the letter by the size of the wig writing it. Ive also had people comment on my personal statement, which I realize is often the first thing an advisor will tell applicants is irrelevant. But I think that it has gotten me some interviews. I have put a lot of thought into this, and I believe its true. I am open to other opinions though.