I use Debian testing on a EliteBook 850G2. I disabled the ATI/AMD gpu since I don't need its computing power, so I don't have any notes on GPU part, but with on board intel graphics, everything is very very smooth. Only non-functional item is the fingerprint reader. I get ~7hrs of battery life with normal system administration / development workflow on a KDE desktop. System runs very cool, and fan seldom kicks in if you push the computer hard.
I've just remembered: I've used the laptop with a Dell U2411 monitor via DisplayPort, a Dell E2211H monitor via DP -> HDMI adapter and HDMI/DVI cable, both without any issues (incl. hot-plug).
I can answer any specific questions if you wish.