Got a new 2011 Mac Mini a few weeks ago and have had nothing but problems with it attached to my 24" ACD. This display worked great on my iMac, and still works great when attached to an older Mini, but on this Thunderbolt port it has three issues:
1. Occasionally, there is a horizontal graphical glitch. This is very minor, though.
2. Frequently, the screen goes completely blank for about a half second or so at a time. Some days this happens rarely, other days it happens multiple times within one minute.
3. Occasionally, the entire screen "scrambles". This video demonstrates this problem. While in this mode, sections of the screen are copied to other parts of the screen, the dock is shifted upwards, etc.
This video shows problem #3, and I move a safari window around while the problem is happening to demonstrate the problem.