Change Your Detergent
The numerous dishwasher detergent options in the supermarket can be overwhelming. Shelves are stocked with various gels and liquids, powders, even detergent in pre-measured packets. These cleaners not only offer to help remove food from your dishes, but also to cause them smell like lemons and gleam like they just came out of a box.
Out of your many detergent options, gel-based cleaners are the biggest stain culprits. Water that isn't hot enough to completely dissolve the gel allows it to cling to dishware, leaving gel gunk all over your "clean" dishes. You can skip using gel-based products altogether (at least in the dishwasher), or use less so it can dissolve more thoroughly.