I'm installing Mtn Lion and I'm wondering what will happen if I format my disk as ExFat and install Mountain Lion on it that way.
Any major advantages or disadvantages to doing this?
Nope, OS X can only boot from Mac OS Extended (aka HFS+) and its variants (journaled, encrypted, and/or case sensitive). I don't have anything to test with here, but I'd be amazed if the installer even let you try installing it on ExFAT.
BTW, this isn't just a matter of "Apple hasn't bothered to support it"; OS X depends strongly on the Posix file permissions model, and ExFAT doesn't support that (just ACL permissions). It would take a lot of work to make OS X work on a volume where you can't have setuid files.