I received a review on my Google Places page but I believe the reviewer incorrectly rated me. What's the best way to contact them if I'm unable to identify their name?

Unfortunately, there's not much you'll be able to do here. Reviews can be left anonymously by anyone on the net. Your best bet is trying to identify the reviewer and get ahold of them to request they update their review through the limited mechanism available to you through the review site in question.

Since you're unable to identify the reviewer by name, you could try posting on their personal profile page on the review site, if it allows for it. On Google, for example, you can click on a reviewers name. If they have their account tied to an email address they check often, they should get the notice once you post on their page. Outside of that, review sites give businesses very little control over their reviews.