The mini wil happily output 720P. Not all TV models are equal though, even with HDMI.
I'm not a TV geek, but I have a friend who has a mini connected to a TV. He actually has 2 HD TVs, and their behavior with the mini attached was very different. One basically just worked (2010 Samsung Plasma), the other (mitsubishi DLP - maybe 2009) was very finicky. After reading the manual, we discovered that the Mitsubishi had one HDMI port that that was configured differently and was better suited to connecting the mini - I don't remember the technical details of the difference. Anyway, even on the 'right' HDMI port, there was a lot of fiddling with the mini's over scan setting to get the picture right.
Anyway, that was a long winded way of saying that you should probably do some research on your specific TV - not just on the mini.