Since I posted the question yesterday, we found out there's more going on than we thought. The dishwasher goes through a wash cycle and then drains and goes into a rince cycle and at that time, food debris seems to be getting back on dishes.
We have a Hotpoint Dishwasher HDA180X-66W. It will go through the drain cycle until it is almost drained, then you hear a click, and it stops draining. We checked the sink drain and it is not clogged. Any ideas of what the problem could be?