The glasses and cups have specks in them that

Maybe try rinse aid like jet dry, some people forget to keep the rinse aid filled up or the rinse aid nozzle gets a encrustation build up from the rinse aid.
Also check your water for hardness, you may need to use a water softener to remove hardness, filter alone will not remove hard water.
One way to test for hard water is with a test tube or something like it and add 2 drops of washing up liquid, and shake the water and soap and see if you have a lot of bubbles or if the bubbles disappear quickly, if there is a lack of bubbles you probably have hard water and may need the mentioned water softener.