As someone who was recently admitted off of my first choice school's waitlist, I would definitely recommend going to the schools, if feasible geographically/financially, and trying to speak to an Admissions Officer. I wasn't able to see anyone when I went to the schools (as I expected) but at least I got to drop off my letter of continued interest in person, which I think reinforced my enthusiasm to attend the schools. Also, I sent letters of continued interest every 3-4 weeks over the past few months. I didn't really have any new accomplishments to discuss, but simply drew out another item on my resume that I felt was strong.
It also doesn't hurt to try and speak to staff members of departments/centers/programs that you're interested in at the particular law school. When I was able to speak to someone in the public interest center, or the international programs department, I had a chance to express my interest in attending the school and also that I was a waitlisted applicant. In one case, the staff member was very straightforward with me about the waitlist situation, which was definitely more information that I was able to get from the admissions staff.