Continuity mistake: Marty and Sherry are looking at old photos to use at Marty's birthday party - we can see one in Sherry's hand that has noticeable brown marks down the back, as though it had been glued in an album. The next shot shows Marty passing this one to her, even though in the shot before it was in her hand. When Sherry passes the picture over to Niles and Frasier, in the shot when they get it, it's not the same photo, as it is clean on the back.
Continuity mistake: When Niles, Roz, Marty, and Daphne are in the living room confessing something shameful, Martin says, "Every time I watch 'The Sound of Music,' I cry." As the shot changes, we see that his hand goes from his arm rest to his lap and his beer can goes from being on one side of the remote to the other.
Continuity mistake: Frasier and Roz are in Cafe Nervosa and Roz is looking at a newspaper while Frasier talks about giving Donny a bachelor party. Roz puts the paper in her lap, but in the next shot over her shoulder we can see that she is still holding the paper up.
Continuity mistake: Frasier's third date, Leslie, shows up at his apartment wearing a long off-white coat. He hangs it up beside the fireplace; for the rest of the scene we sometimes see the coat hanging with the left sleeve straight and sometimes with the left sleeve all crinkled up.
Revealing mistake: During the scene where Frasier is dropping Charlotte off at the train station (the first time) you can see the background behind him shows that the car they are in is turning left. Yet we can see his hands on the top of the steering wheel and during this time he never turns the steering wheel.