Continuity mistake: Frasier is off to find Niles and he tells Martin to come with him. Marty puts his chair down as he says "I don't want to go to Niles'" - the shot changes and we see him lower the chair again. His coat in his lap also changes position between these two shots.
Continuity mistake: Donny is sitting on Frasier's couch eating Chinese food. One of the containers, with chopsticks in it, is sitting on the table, near the center. In the next shot the chopsticks have disappeared and the container has moved towards the end of the table.
Continuity mistake: Early in the show Frasier finds Daphne's engagement ring which she had misplaced. He is holding it - on the table we can see a chip bag that Daphne had used to hide her ringless hand. During the course of the scene, the chip bag appears and disappears several times.