I have a base model i5 2.3Ghz mid-2011 Mac Mini connected to a 23" Samsung 1080p LED HDTV/Monitor via HDMI ports (HDMI cable) and it works flawlessly. I have no problems at all with the image, colors or sleep mode...whether I am in OS X 10.8.2 or whether I left the Mac on with Windows XP or Windows 8 Pro in Parallels 8 virtual machines. The Samsung monitor via HDMI turns off as the scheduled time regardless of what VM or state the system is in.
I use the Samsung remote to switch between the Mac Mini, an older Windows XP Pro PC on the VGA port, a Sony Blu-ray player and cable/satellite TV. I am curious to know if the newer Mac Mini late-2012 models with the Intel 4000 graphics offer the same flawless compatibility with the newer Samsung combo LED HDTV/Monitors as my mid-2011 with the Intel 3000 graphics. I am considering purchasing a new late-2012 model Mac Mini and a newer Samsung 40" or larger LED HDTV in the near future (I prefer the 6500 and up models with SmartTV and 3D capability).