That's a simple question to answer: Unfriend him! As the administrator of your law firm's Facebook page, it's well within your abilities to make a hostile commenter disappear, or if that's not practical, at least to delete his comments as soon as they're posted. On your own Facebook site, you are the master of your domain, and there's no reason to put up with an annoying or intrusive guest who may repel other, more loyal, clients.
Matters are different, though, if you notice a discussion about your law firm taking place on someone else's Facebook page (which you have access to, of course, only because you have “friended” or “liked” that firm yourself). Since you are unable to delete the offending person's comments, it may seem like your only recourse is to join the discussion and defend the honor of your law firm. More often than not, this strategy will backfire; some Facebook users really like to get into arguments, and you have better things to do with your time than to carefully and factually debunk everything this “troll” has to say.
A better solution would be to maintain a dignified silence and let other participants come to your aid. In the last resort, you can always send a message to the administrator of that Facebook page and ask him to unfriend that individual (though of course he's under no obligation to comply with your request!)
The basic fact is that, in order to prosper in the world of social media, you have to develop a thick skin and not take every derogatory comment about you or your law firm to heart—otherwise, you'll be spending all day posting on Facebook rather than working billable hours on behalf of your clie