I've been having this problem ever since OS X 10.8, even after adding git to my path. It turns out that if I launch Sublime from the Terminal (subl .) I get no Git path errors. But Launching the app via the dock doesn't pick up the path settings and I get the error every time. This post leads me to believe that this can be solved but it's not clear to me how to use the .plist syntax to do it.
UPDATE: I uninstalled git (brew) and reinstalled. Brew doctor scolded me to install CLI tools, so I downloaded the ML version and reinstalled that too. Finished with brew install git, and now SidebarGit works as expected regardless of whether I launch from Terminal or Dock. No Path errors yet.