Agreeing with most of the other posters: knowing people who have influence with the adcoms helps. It doesn't hurt to take advantage of meetings with deans, or other higher ups. You aren't going to say "I will do anything to get into your school", but it is perfectly fine to say "this is my background/my experiences/my grades/my scores/etc.--what do you think my chances are for getting into your school and what do you think I could do to improve my application?" You aren't directly asking them for assistance in voting for you to the adcom, but you open the door for dialogue. If the dean or whoever likes you, then they will certainly put in a good word for you to the adcom.
A good word to the adcom doesn't guarantee that you'll get in, but it certainly can't hurt.
I know a few influential people at my state medical school (one was on the adcom), and I know almost for a fact that they made sure I got in and received a hefty scholarship offer. I might've taken it if I didn't get into Mayo (or a couple of other top schools). They were a little disappointed that I didn't decide to go there, but can understand my situation.
Talk to your contacts. Start dialogues. Tell them about your interest in their school and about your great ECs. It can't hurt any.
Good luck! :wink: