While Eclipse does work across multiple monitors, I know of one bug that I find quite annoying.
I use 3 monitors, with the main source view occupying my center screen, and the output console occuping the left screen, and all the misc views (outline, problem view etc) taking up the right monitor.
The bug is that when your screen saver kicks in, eclipse resizes itself to fit in one screen, so you have to reset your workspace when the scrensaver goes away.
here is the bug if you want to vote for it to get fixed:
