Plot hole: When Frasier is trying to get to the bottom of Niles' problem viewing Daphne in a real way, we see them both against past scenes in the show; Frasier watches and comments on some of them as he talks but because he is actually only discussing these events with Niles, he shouldn't be able to see a visual of anything such as the dress Daphne is wearing during the dance scene.
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.
Continuity mistake: At the beginning of the show, Niles, Frasier and Daphne are at Cafe Nervosa. Daphne is standing up talking to Eric the server and Niles gets agitated, and spills sugar everywhere. Eric throws down a dish towel so they can clean it up. The dish towel appears and disappears several times during the scene.
Continuity mistake: Early on in the show, Martin is trying to get Eddie to shake a towel off his head while Daphne stands behind the dog, folding laundry. In one shot she is standing with the folded towel over her arm; in the next shot she is folding it again. When she goes to the door, there is something red on top of the laundry basket, but when she returns the towel is back in the laundry basket (it's not the towel Marty put on Eddie's head: that's sitting on the coffee table).
Revealing mistake: The view from Frasier's apartment shows the Space Needle prominently in the background, however, the elevator that takes visitors from the ground to the observation deck is frozen in time midway to the top. This was corrected after the first season.
Continuity mistake: At the beginning of the show, we see Marty add some beer to his champagne glass until it's almost full - just then Bulldog grabs his SeaBee award from the coffee table and now Martin's glass is almost empty, even though he's had no chance to even take a drink.
Continuity mistake: In the opening scene, Niles goes to pour sugar on his spoon and the top of the sugar dispenser comes off and disappears - it looks like it goes into his lap. We don't see the top again until after the teenager says, "Aren't you going to yell at them?" and suddenly it is in plain view, on the right of the table.
Continuity mistake: In the show from Series 7, "Big Crane on Campus", the Jean Smart character is introduced as Lorna Lenley - ex-prom queen from his high school with a volatile personality who has a brief relationship with Frasier. In Episode 21, series 8, she comes back as the same character - ex-prom queen, had a fling with Frasier, etc. - but now her name is Lana. She was billed as Lorna in the series 7 show and as Lana in the series 8 show. The names may be similar but are definitely different names.