One of the themes of my essay will be my diverse academic background and my interest in intellectual property law. Do law schools care?
This worries me for two reasons.
First, 'one of the themes' suggests that there are at least two themes. That's at least one too many. Your personal statement should focus on one theme; there's no way you can possibly develop two themes well in a two-page essay. Maybe you can pull it off for Berkeley.
Second, talking about your diverse academic background creates two problems. First, it sounds like you're just rehashing/highlighting specific things from your resume. Second, it sounds like I can already get that information by looking at other pieces of your application. Your personal statement shouldn't do either of these things.