I upgraded to Mountain Lion yesterday, as I like to torture myself a little from time to time and see what an OS upgrade will break this time. I’ve only two things that didn’t work, Mailplane and Parallels. Mailplane needed to be upgraded to either version 2.x preview or to the Mailplane 3 beta.
Parallels also had an upgrade with support for Mountain Lion and installing that got it working.
I have two 24" monitors on my Mac and I run Parallels full screen on my 2nd monitor. On the new version with OS X Mountain Lion, when I click inside the VM, apps on my main display start flickering like crazy. There is a forum post on it here, but basically the fix for now is to disable 3d acceleration on your VM.