Matt, mostly all software (if it ran on Lion) will run fine on ML. The only one I know of that wont is Little Snitch, which needs a small upgrade. Although, you can still download the LS trial from their site for free, which runs in 3 hr stretches, and then you have to start it again.
Ive installed ML and all on my applications work just fine. Some of them will download small updates, which are free, but essentially if it ran on Lion, it will run fine with ML.
If youre worried, check this out:http://roaringapps.com/apps:table
Although a lot of those incompatibilities came about way before ML. Basically when MacOS stopped incorporating Rosetta, which if memory serves correct was two or three OS's ago.