Moon Dance - S3-E13
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).
To Thine Old Self Be True - S7-E20
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.
Morning Becomes Entertainment - S7-E19
Continuity mistake: At the beginning of the show, Frasier and Daphne are talking in Cafe Nervosa and behind them there is an extra at the counter. In some shots he is sitting there doing nothing, and in others he is eating a muffin.
When a Man Loves Two Women - S6-E21
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.
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: At the beginning of the show, when Bulldog throws a cup of coffee in the direction of teh armed man, the cup rolls to the floor, but when the shot shows Bulldog getting up from the floor, the cup is lying on the edge of the counter.
Fool Me Once, Shame on You, Fool Me Twice... - S2-E14
Continuity mistake: Daphne is visiting KACL and has Frasier's headset up to her ear and then down on the console in a split second, with not enough time to do this naturally. (00:13:45)
Continuity mistake: At the start of the show Niles is playing the piano. He turns to talk to Frasier and his hands are in his lap, but in the next shot one hand is back up on the piano keys, with no time for this to have happened naturally.
Forgotten But Not Gone - S8-E18
Continuity mistake: While Marty and Frasier are eating Fredericka's cooking, Frasier puts his knife down on his right, then switches his fork to his right hand. After he says "motion carried," the shot shows his fork back in his left hand.
Frasier Crane's Day Off - S1-E23
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.
Guess Who's Coming to Breakfast - S1-E13
Continuity mistake: Marty, Elaine, and Frasier are sitting down to breakfast. Elaine picks up her mug and in the next shot we see her reach and pick it up again.
Continuity mistake: While Frasier and Niles are having coffee outside at Cafe Nervosa, a red napkin is by Frasier's cuff. In the next shot it is suddenly in the center of the table, even though no one touched it.
Roz's Krantz & Gouldenstein are Dead - S4-E15
Continuity mistake: Frasier is on the couch talking to Niles. As he says "I simply release my humble words", his hand switches from being around the middle of his bottle of water to being around the neck, with no time for natural change.
Continuity mistake: Daphne comes into the Cafe and asks Marty, "Where have you been?" and her purse is on her right shoulder. In the next shot her purse is in her hand, but not enough time had passed for this to happen naturally.
Roz's Turn - S4-E17
Continuity mistake: When Frasier, Roz and Bebe are arguing, Frasier says something like "she has no reflection." When he says this you can just see Bebe's hands in the shot and they are clasped together. In the next shot they are instantly quite far apart.
Continuity mistake: At the end of 3-10 in the airport with Kate, Frasier says that he has an allergic reaction to cats but here he cat sits for Mr. Bottomsly.
Suggested correction: This has been addressed in the Questions section. Frasier is apparently choosing to deal with his allergies, in order help the cat's owner. It's also possible for allergies to be triggered by one cat, but not another. It depends on the amount of dander that the particular cat produces, and the level of Fel D. 1, a protein in their saliva.
Liar! Liar! - S4-E10
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.