As is the case with any major Mac OS X update, third party apps may have to be updated for compatibility with Mountain Lion. The best resource, recommended all over my Twitter stream and various tech blogs – is RoaringApps. Type in an app name and see if it’s confirmed ready for the 10.8 switch.
With the last few Mac OS X releases, I’ve gotten progressively less and less worried about app compatibility; when in doubt, it works. That said, for critical apps, a quick check over at RoaringApps is well worth your time.