We had a maintenence plan for the first 5 years of our dishwasher, at that last yearly checkup, it was doing the same things you described, I asked the maintenence guy about it and this was his advice:
Use powder detergent (at the time we were using liquid/gel), it distributes more evenly and dissolves in the water better.
Use about half of what the detergent cup will hold/what the detergent directions say to use, even for big loads, too much just leaves residue, He said, remember the detergent companies are just rying to get you to use more to sell more to you....he said the same goes for washing machine detergent.
Don't pre-wash dishes, just scrape off big chunks, and maybe run the plates under some warm running water - no extra soap/scrubbing - the soap needs the food debris to help it activate/do its job better.
Also told us we could run an empty cycle with vinegar or even with CLR, to get the residue on the inside walls of the dishwasher all cleaned off.
Good Luck - these tips have worked great for us!