Q. Can I store used dirty dishes in the dishwasher to keep the kitchen clean during Shabbos (if no light goes on or off)?
A. Poskim permit storing dirty dishes or soiled clothing in a washing machine if the purpose is to keep clean the house and not to prepare or set up to save time after Shabbos. (Igrois Moishe 4: - 39 Melochos p. 115 et. al.).
Mishne Halochos (4: 43 and 4:44) explains that there is no “ma'aras ayin” prohibition involved by placing oneself in a situation where an onlooker may suspect that one is about to wash the dishes or the clothing on Shabbos, if customarily during the weekdays one also stores away the dishes and washes them at a later time, when the machine becomes full.
Horav Shlomo Miller also advises not to place on Shabbos the dishes each one orderly and separately inside the racks, ready to be washed, but rather to just pile them up and get them out of sight.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a