I have gotten into two schools off of the wait list, and as far as I can tell, it is sort of a crapshoot...For one school, I did absolutely nothing but check off "yes, i will remain on the wait list". For the other, I sent in a Letter of Continuing Interest, wrote an additional essay on why I want to go the school and what I could contribute, and had an alum who is a family friend send in an additional recommendation. The alum did not attend the law school, but another graduate school there. I also expressed that they were my first choice and I would absolutely attend if admitted.
I think that visiting schools and scheduling an appointment with an admissions counselor could also help.