For reasons related to special needs adolescence I researched the use of a kiosk-mode browser on a Mac.
The short answer is - there are no free options. There's not much of a market for this on OS X, and even browsers that support kiosk mode on Windows 7 don't do it on a Mac. Opera used to support kiosk mode in OS X, but the available documentation is out of date and when I tried the kiosk mode command was not recognized. (Opera for Mac is basically dead.)
Several older posts mention Saft for Safari -- that product has been abandoned and doesn't run in modern Safari.
eCrisper for Mac is not in the app store, but it is still sold for $79 with a very restrictive license. Since it's not in the app store I would worry about Mountain Lion compatibility.
Running Chrome with extension in kiosk mode, particularly if combined with SimpleFinder and single app execution might come close for some purposes.