So far the only 3rd party programs (non-MAS) that I've tried on ML has been Photoshop and Premiere Elements 10 Suite, Minecraft, Nocturne, and Screenflow.
Elements 10 Suite worked fine. I ran into a small hiccup with Premiere, the top grey bar with the Close, Minimize, Maximize buttons didn't appear. Starting a new project brought it back.
Minecraft, I didn't really play it, just started it up and entered my world, then left. It seemed to work fine, just needed to download Java again at 66MB.
I have Nocturne set to start upon start up, and it worked just fine.
Screenflow started up fine, I didn't record anything though.
I'll get to mess with more programs tomorrow.