LG displays are not compatible with the new minis.
I have tested the i5 2.3g , i5 2.5g Mac minis with the LG 32ld450, 32lv3510 TVs and a LG monitor, a Dell monitor.
When I connect a display to the mini's HDMI port via a HDMI cable, the image quality is bad.
It's not sharp, not clear. Overall it's unusable.
When a display is connected to the thunderbolt port using a mini-dp to dvi adapter, it's good, normal.
But whe I connect two displays at the same time(one to the HDMI, the other to the thunderbolt),
the mouse cursor movement become very laggy, sluggish, and jumpy. So I can't use dual displays which I should use.
I have been using these TVs and monitors with a late 2009 Mac mini with no problems at all.
I think a Dell monitor works well with the new mini, but LGs don't.