This answer is based on Mercurial experience, not Git, but this experience says using Dropbox this way is asking for corrupt repositories if there's even a chance that you'll be updating the same Dropbox-based repository from different machines at various times (Mac, Unix, Windows in my case).
I don't have a complete list of the things that can go wrong, but here's a specific example that bit me. Each machine has its own notion of line-ending characters and how upper/lower case characters are handled in file names. Dropbox and Git/Mercurial handle this slightly differently (I don't recall the exact differences). If Dropbox updates the repository behind Git/Mercurial's back, presto, broken repository. This happens immediately and invisibly, so you don't even know your repository is broken until you try to recover something from it.
After digging out from one mess doing things this way, I've been using the following recipe with great success and no sign of problems. Simply move your repository out of Dropbox. Use Dropbox for everything else; documentation, JAR files, anything you please. And use GitHub (Git) or Bitbucket (Mercurial) to manage the repository itself. Both are free so this adds nothing to the costs, and each tool now plays to its strengths.
Running Git/Mercurial on top of Dropbox adds nothing except risk. Don't do it.
