I've just finished Mountain Lion upgrade on my build and want to share it with other users. The described below was the same I've been using since SL:
Motherboard: Intel DP35DP
Memory: 8 GB (4 Kingston 2GB DDR2 800MHz PC2-6400 KHX6400D2/2G)
Display Adapter: Sapphire ATI Radeon HD...
I've found a way to have dual monitors (HDMI + DVI) in Mountain Lion using a Gigabyte Radeon 6670.
First of all, I followed the installation procedures in here: