So I've gotten through most of the game. I've gotten to the point where the clan has all the equipment, and I see the cinematic about tracking them down to a desert location... and then the game kicks me to the main menu. No idea what's happening. Can anyone help?

I don't know what's causing this, but Klei suggests to re-install the DirectX runtime, when there are crashes during cutscenes.
Here's the download link: http://www.microsoft.com/en-us/download/details.aspx?id=8109

As Mark of the Ninja uses an automatic save system you're screwed if the savegame is corrupted because there's no backup. You can still try to backup your current save and re-install the game. The savegame and settings are usually stored in this folder: \Mark of the Ninja\users\

It also doesn't hurt to run the game in compatibility mode for Windows XP with admin rights. You find those settings by right-clicking the game's shortcut, select Properties and go to the Compatibility tab.