The deposits on the dishes are likely to be food debris left on the dishes during rinsing and then baked on hard during drying.
To stop it happening do the following.
1) Rinse off the worst of the food debris before loading the dishes into the machine.
2) Use a good quality Liquid Rinse Aid in the machine and avoid the three in one tablets.
Rinse aid is not to make the dishes shiny - it removes surface tension in the water to aid draining.
Notice the manufacturers provide a compartment for liquid rinse aid - they would not do so if there was no reason to do so.
What you're finding on the dishes is very likely to be what you've put into the machine...
Good Luck..., February 2016