Continuity mistake: Frasier is having a glass of sherry, sitting on his couch, talking to Niles and Martin. As Marty says "let's go have dinner", Frasier throws his hands up - in real life he would have still had the sherry in his hands. There was no time for him to have put it down.
Continuity mistake: During the opening credits Roz and Frasier are sitting on his couch working. Roz is telling him that she has a date the next day - he is holding a magazine. But as she says "a month", the shot goes back to Frasier and he's holding papers rather than the magazine.
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.
Continuity mistake: In Cafe Nervosa, after Niles has taken off all his clothes, Frasier wraps him up in a couple of Cafe Nervosa aprons and Roz picks up Niles' clothes from the floor. In one shot, we see his tie towards the top of the pile in Roz' arms, and in another it is swinging free at the bottom of the pile. The clothes change position in her arms from shot to shot. In one shot the boxers are still on the table, with a newspaper. In a subsequent shot, Roz has the boxers. When Niles is being taken outside, the table nearest the door has only a cup on it. In the next shot, we see the newspaper on the table again.