I've had the hardest luck Googling this, because "dirty dishes" implies that there are still bits of dirt on the dishes themselves. My dishwasher does usually get everything off--cheese is about the one thing it can't handle. The problem is that there will be flakes of dirt leftover. It will dry into the face-down-cups and pool in water left on stuff in the top rack.
I assume the problem has something to do with drainage, and that this stuff is left around when the dishwasher starts rinsing. The dishwasher connects to me disposal through a flexible, corrugated tube. It seems to come out towards the bottom back of the dishwasher into the in-sink-aerator's dishwasher port.
There wasn't much tube to play with, but I managed to loop it around itself and tie it together that way. This hasn't helped the problem. What should I try next?