I found out about Kdenlive from Mint's Forum's web page. It says it's for KDE, but will it work on a GNOME desktop?

I can say that the older versions will work, and do work on my ubuntu 8.04 desktop(which I believe mint is based on). However, I have a problem with no sound waveform being displayed. Other than that, you should be fine.

Kdenlive 0.6 and 0.7 work perfectly on a Gnome Desktop.

You only need Kde4 dev environment installed.

See this screenshot :

version 0.8.2.1 working fine for me on Linux Mint (10) using Gnome2 desktop

On gnome 3 kdenlive worked, too. But pop-up dialog windows are not draggable indepently from the main window due to gnome 3's window management. That can be annoying sometimes.
Tested until kdenlive 8.1 , then I switched to KDE