The EyeTV software is normally used full-screen when watching a show, but I've found that it's easiest to use the OS X GUI to scheduling recordings. This is difficult to do as my TV uses 7" CRT tubes to generate the display, which limits the horizontal resolution to something between (if I recall correctly) 1300 & 1400 pixels which results in hard to read text. The next model up from my HDTV used 9" CRT tubes, and it was able to resolve the full 1920 across the screen, but that was not within my budget. The other problem is the interlacing (that's the i in 1080i) causes a lot of flicker, which also contributes to making it difficult to read.
OS X supports something called HiDPI, which is used to drive the new Retina Displays. Basically the OS treats the resolution at half in each direction and draws each "virtual pixel" using 4 real pixels so everything appears to be twice as big. Text and HiDPI aware programs will use all 4 real pixels and generating high quality images. 1080i is 1920x1080, so switching to HiDPI means it'll treat it like a 960x540 display.
The HiDPI settings were initially hidden, so I entered this on the command line to enable them:
sudo defaults write /Library/Preferences/com.apple.windowserver DisplayResolutionEnabled -bool YES; sudo defaults delete /Library/Preferences/com.apple.windowserver DisplayResolutionDisabled;
The HiDPI option showed up but when I selected it the mini switched to 50 Hz for some reason, which my TV doesn't support. Remoting into the mini I changed it back to 60 Hz, but then it would switch back to 1080i instead of HiDPI. I went around and around with that for a while, which was rather frustrating. I then found a shareware utility, SwitchResX, that let me select HiDPI at 60Hz. Works great, so I registered it.
Using HiDPI also reduced the amount of flicker.
I have discovered that the Aggregate Device causes AirServer to output noise instead of the whatever audio is sent from the iDevice. I haven't looked at it very much, but did find that switching the Sound Output back to just HDMI cleared it up. I hope to find a fix for this so I can leave audio out using the Aggregate Device.