I own a GE Profile Trition quietpower III GSD5940F00SS dishwasher. The dishes, particularly the mugs and cups, are not getting clean.

Your sprayer arms may be clogged. You can remove them by loosening the screws holding them in place. Flush them with the sprayer at your sink. If you can SEE residue (parts of paper labels, bone fragments, fruit peel pieces, etc) remove them with a tweezer.Reinstall the spray arms and see if that works.
Three more ideas:
(1) run a cycle without dishes OR detergent and use 1/4 cup of white vinegar instead. This will break down soil and "gunk" and help your dishwasher run more effectively.
(2) use an old toothbrush and clean the underside of the door INSIDE the dishwasher. The door will be open and you just brush the bottom of the open door on the INSIDE of the dishwasher. A lot of "crud" gathers there and can be redeposite on your dishes. We seldom think to check that area.
(3) the pipe that carries water to the upper sprayer arm MUST fit against the outlet in the back of the dishwasher. If it is dislodged or not seated properly, the water won't flow to the upper sprayer arm.
Hope one of these suggestions helps. If it does, please rate my suggestion. Thanks.