I am having the exact same problem on my Mini.
I looked at some SS of people with a similar sounding problem, but their pics look alot "worse" than what I am experiencing.
On black screens I get a constant "flicker" of lines. Usually they are green, but sometimes they can be blue or red (or at least I "think" they look blue or red).
I wonder if it's not the Dual-Link DVI adapter. I had this monitor on an older, slower computer and didn't see the lines.
Since I rarely need black on my screen, I just changed the desktop picture and the problem is "solved."
But still, a $3,000 monitor (back in the day) with a $100 adapter cable on a brand new computer shouldn't have any issues, imo.