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).
Continuity mistake: Niles comes into Cafe Nervosa holding a newspaper and begins to talk to Frasier and Roz. As he says "mere words cannot", the shot changes and the next shot shows the newspaper has flipped over to the other side in his hand. He didn't have time to do this naturally.
Continuity mistake: When Manu pulls down the metal front over his kiosk, Frasier has his umbrella in his right hand. By the time Manu pulls it all the way down and catches his hand under it, Frasier's umbrella has shifted to his left hand, even though he never transferred it.
Continuity mistake: Near the beginning of the show, Daphne comes home from shopping holding a bag of groceries with the leafy tops of vegetables facing out. Frederick goes to help her and suddenly the leafy tops are facing inwards, without Daphne having time to move the bag.
Continuity mistake: When Frasier and Niles are in the cafe, Niles says "So what was Fay doing at your apartment last night?" When he says this, you can see he has just started to stir his coffee with a spoon. The shot then changes and the spoon has vanished.David Mercier
Character mistake: In the scene where Jerome Belasco turns up unannounced at Frasier's apartment, Daphne tells him she's psychic and guesses that he's an osteopath. After Jerome leaves, Daphne says she thought he seemed very nice. Frasier turns to her and says, "This from the psychic who said he was a chiropractor."
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.
Continuity mistake: Martin and Frasier are having breakfast and Marty is making fun of Frasier's radio audience. In one shot Marty's arms are folding on the table in front of him over his newspaper - in the next shot one arm is stretched out over the newspaper and the other is at 45 degrees angle in front of him.