USNews offers stability only as far as the accuracy of numbers volunteered and the strength of criteria used to rank schools. That said, I don't think a 2nd tier school would drop to the 4th tier unless they had a reporting error, but as it's been said over and over again on this board, yes rankings matter but not to the degree that you can compare a rank 50 school with a rank 53 school. It's pretty obvious that even if there are law firms that pore over the minute details (i.e. School A > School B because School A is one higher rank than School B), they'd just be changing their opinion again when the next year's edition comes out. The rankings are most useful (and this is relative) to determine what schools should be clumped together in terms of quality. For instance, 1-5, 6-20, 21-40, 41-70, etc.
In response to the bit about firms asking where you studied law, one needs to use a bit of common sense to determine the reality behind it. Yes, they will want applicants from top 10 schools or tier 1 schools, etc. However, I'm not sure that they would nitpick as to deny Tulane applicants this year simply because the school is ranked 50-something. Firms probably have an idea of the usual T1 schools, etc., and it would be stupid to frown upon a school that is ranked 51st in one year and smile upon it because it is ranked 50th in another. Why is it stupid? Because the data is from two years ago, for one, and the usual rant about the USnews rankings apply here as well. Firms have a much better indicator of school quality in the form of its hiring process, and they also like to hire from local schools. Cali firms, for instance, probably won't take Kentucky grads over Loyola grads, even though Kentucky is ranked higher. If they've been hiring from Loyola in the past, they know what they will get from Loyola, and most likely, there are partners at the firm who are from Loyola.
What I'm basically trying to say is USNews rankings do matter but in a more general sense. By asking yourself questions like "if my school was T2 when I attended and T1 when I am applying for a job, am I a T1 or a T2 grad?" you'll be able to discern what's important and what's not. Unless you get into a truly national school, the region of the school is probably the factor you should weigh your decision heavily upon. I bet every region already has an idea of how schools are compared to one another, no matter what USNews says.