A Midwinter Night's Dream - S1-E17
Continuity mistake: Early in the show Niles shows up at Frasier's in his pirate outfit. He has a plastic knife in his sash which changes position noticeably several times during the scene (without Niles touching it).
Roz, a Loan - S6-E9
Continuity mistake: Roz gives Frasier a gift of a decanter which he takes partially out of the box. By the next shot he has it back in the box and out of sight; with no time for this to happen naturally.
Continuity mistake: As Frasier and Niles are starting work on their book, Marty gets four snacks and a beer and sits down in his chair. He gets up and we see the two bags that were behind the beer and can of something are now in front of them. Marty never touched them during that time.
Continuity mistake: In one of the sequences where Niles and Shenkman are running in and out of the bedroom, Shenkman sprays perfume around the bed. The roses that were on the pillow have now completely disappeared and never reappear although neither Niles nor Shenkman touched them.
Continuity mistake: When Frasier is in his booth with Bulldog lecturing him about his phony hero status, Bulldog is eating a cookie that goes from being semi-circular to having a large round bite out of it and then back to being semi-circular again.
Hot Pursuit - S7-E18
Continuity mistake: Early on in the show, Roz leaves yellow papers neatly on Frasier's coffee table and leaves. In later shots, while the others are talking, we see the papers become scattered - even though no one goes near them.
Continuity mistake: During breakfast, there is a bowl of scrambled egg next to Martin that moves itself around, and at one point the fork in it just vanishes and then reappears.
Frasier's Imaginary Friend - S5-E1
Continuity mistake: When Frasier gets up to get out of the plane seat between the married couple, he is clutching his coat and boarding pass in his left hand/arm but when he reaches the aisle, they are in his right hand.
Selling Out - S1-E9
Continuity mistake: When Frasier and Niles are in the Cafe, Niles says something like "Why do you feel like that?" During this line Niles goes from putting sugar in his coffee to having the mug raised instantly.
Continuity mistake: Marty is sitting at the dining room table and for a couple of shots he's eating potato chips with his right hand; the shot changes to him eating with the other hand, with no time for a natural shift. (00:14:50)
Three Faces of Frasier - S7-E21
Continuity mistake: When the first cartoon is about to be revealed, the cloth over the easel moves up and down between shots.
Continuity mistake: After calling Martin the "Sultan of Brunei," Frasier grabs his wine glass with one hand on the top and walks out of the kitchen. In the next shot when he is coming out he is holding it by the neck and there was no time for him to change his grip.
Continuity mistake: When the vase is broken during the swordfight, notice the way it has been damaged. When Niles comes back down the stairs, the damage to the vase is different.
The Last Time I Saw Maris - S3-E8
Continuity mistake: Frasier and Niles are in the living room talking about Maris. Frasier says, "I was on the mark", and Niles' beer stitches from his right hand to his left from one shot to the next.
Merry Christmas, Mrs. Moskowitz - S6-E10
Continuity mistake: Niles and Marty are in the kitchen and Niles is coaching Marty on how to pretend to be Jewish. While they are talking, the lid on the sugar bowl goes from being on properly to being askew, even though no one touched it.
Continuity mistake: Martin and Daphne are laughing at Eddie who has taken a pill to calm him down - in one shot he has a paw up in the air, but in the next shot both paws are pointing sideways. The shot changes again, and Eddie is back in the first position. He had to time to change naturally.
Continuity mistake: Frasier has left his mug on the table to goes to console Father Mike who has just come out of Kate's office. The next couple of shots of the table show the mug in different positions.
Martin Does It His Way - S3-E3
Continuity mistake: When Martin first brings the sheet of paper out of the box with the lyrics to his best song on it, the paper has a section torn out of one corner. A couple of shots later and the paper is whole.
Answer: In the last episode, they explained that Tossed Salad and Scrambled Eggs is a metaphor for the mixed-up people to whom Frasier dispenses his radio psychiatric advice.