my main worry with video in would be if you plan on saving it (encoding on the fly is already a bit hard if you plan on going hd), but also, right now, writing on the sd card is a cpu intensive operation (at least in my tests).
as far as displaying a video in goes, that shouldnt be a problem, so long as you can compile some linux drivers (if there is some sources it should be possible).
Now the issue i could see with using that for remote control would be, how much reaction time are you planning to get.
most tv tuner will get quite a few seconds delay, i cant say i tryed that many, but from my personal experiences, i would usually get a delay of 2-3 secs between the input and the display.