Common problems in order of commonness/ easiest to fix
1- Make sure the disposal is run and clear
2- Check the trap at the bottom for sediment & or debris
3- Check the wholes in the spinner as well
4- Make sure the hose leading from the washer to the disposal is clear
If any of these are partially clogged... the dirty water doesn't entirely empty out... and so the heavy bits (that are kind of like sandy bits) just continue to get swirled around. Frequently, they're on the other dishes as well, but are so fine (and typically bleached transparent) that they're only visable on clear glass. And then it's obviously "eeew".
The same problem can happen if there's not enough water pressure, or if your pump is on it's last legs.