CTlawyer- I think I can picture it even without the picture. Pretty cool device, seems like they thought of everything!
the milk/meat question would be one for the Rav. Of course this particular problem could be avoided altogether if you listen to health recommendations and only defrost your meat in the fridge. (Confession, I do it all the time too- it takes days to defrost in the fridge).
Another non-kashrus reason for 2 separate waste pipes- kitchen pipes tend to get clogged, from all those fatty food bits that stick to the sides. I would imagine that 2 separate pipes would take twice as long to get clogged as one.