The fine debris will be broken down food particles suspended in the rinsing water and baked on hard.
The solution is to use Rinse Aid - it helps the rinsing water to drain off in sheets rather than forming droplets.
Rinse the worse food from the crockery before loading up and use a liquid rinse-aid product.
You can also buy cleaning tablets - I have no idea if they're any good but a couple of cycles with no crockery may help to clear the pipes.
Good luck...
Peccavi, March 2013