I have a macbook 2.0 Core Duo and it ran a 1080i file with digital audio with 512mb ram.
Now i have 2gb of ram, the only difference is that it starts slightly smoother. The res it outputs to my HDTV is 1360 x 768, so im missing a line of 6 pixels for the HDTV native res of 1366 x 768.
Id be interested to know if the mac mini could output 1080p's full resolution.