Yes - I know the cause and the solution - it has happened to me.
The dirty bits you see on the crockery are tiny bits of food debris that you yourself have put into the machine. Food items break down into small particles and are deposited on the crockery in the rinsing water - then they get baked on hard during the drying process.
Rinse aid helps the rinse water to drain off in sheets - without rinse aid the food particles remain in water drops and become attached to the dishes.
Rinse off the worst of the food debris before loading the crockery into the machine - use a good quality rinse aid liquid - ensure adequate dishwasher salt - avoid the less efficient multi purpose tablets.
I used to have the problem you describe - but not any more.
Good Luck...
March 2016