The dishwasher appears at the beginning of the episode when SpongeBob is seen using it during his night shift. As his surroundings start to spook him he washes all of the dishes in the quickest amount of time possible and tells Mr. Krabs he will be leaving.
SpongeBob uses the dishwasher conveyer belt in the kitchen as a bathtub to clean the ketchup and mustard stains off of his shirt. Squidward enters the kitchen, holding a bucket of dishes to insert into the dishwasher but then realizes it is jammed. He reaches in the machine to retrieve the dishes clogging the machine, only for SpongeBob to turn out to be bathing there.
"The Krusty Plate"
It appears when SpongeBob says "Now everybody's all clean and ready for beddy-bye" to the dishes.
After Mr. Krabs thinks SpongeBob knows his secret about his split nail, he washes dishes and breaks said nail.