Continuity mistake: Late in the show, Frasier throws his notebook on the coffee table and it lies flat near the books. A couple of shots later, it is on top of one of the books, with pages flipped back. No one went near it in the meantime.
Continuity mistake: As part of his divorce settlement from Maris, Niles gains ownership of Shady Glen, Maris' mountain home. After this episode, Shady Glen is never seen or mentioned again. What's even odder is that Niles and the rest of the characters over the years go to mountain cabins, which makes no sense because wouldn't they just use Niles' place?
Continuity mistake: Frasier goes into the kitchen to get Niles some water; he gets an empty glass goblet, then opens the fridge and takes out a bottle of water and then it cuts to the glass sitting on the counter already full of water.
Continuity mistake: Niles puts the cap of the solvent can on the coffee table but a couple of shots later it has moved about 8 inches away, even though he didn't touch it. (00:04:10)
Continuity mistake: Niles leaves the kitchen with a small tray of devilled eggs to serve his guests - as the shot changes to him coming into the dining area, he is carrying a different tray, with different appetizers on it, including some grapes. (00:08:35)
Continuity mistake: During the part of the show where they are getting ready to play Murder we can see empty punch glasses on the table - in another shot we see three even though no one went near them. This changes back to 2 after the lights come on - unlikely anyone helped themselves to punch when the lights were out.
Continuity mistake: If you look closely at the couch in the first scene ("A Valentine for Niles") it is not the same couch used during the rest of the run of Frasier - it looks brand new and it doesn't quite have the same texture or look. It makes sense, as Niles sets fire to the couch at the end of the scene.
Continuity mistake: When Frasier is saying goodbye to Mr. Rugly, he knocks over Mr. Rugly's coffee mug with his umbrella. The mug is tipped off the table but in the next shot Mr. Rugly grabs it - but in real time, by this point the mug would have already hit the floor.
Continuity mistake: During the closing credits, Roz is sitting at in Cafe Nervosa with her little black purse on the table. While she is preparing her coffee and flirting across the room at a guy, her purse disappears from the table for the rest of the scene.
Continuity mistake: Niles runs into the kitchen where he finds Frasier cleaning the oven. As Frasier stands up, one of the cuffs on his rubber gloves has been turned over, and the other hasn't. A couple of shots later they are both neatly folded over. As Frasier leaves the kitchen, they are back to the first position. At no time did he adjust them.
Roz, a Loan - S6-E9
Continuity mistake: Martin was holding a little blue bag on Eddie's head to comfort him; when he gets up he tosses it on the coffee table, but when the shot changes it is sitting several inches away from its original spot.
Continuity mistake: Niles throws a long white cloth over his shoulder and heads for the kitchen. When he reaches the kitchen the cloth is much shorter in back than it was the shot before. (00:04:40)
Shutout in Seattle (2) - S6-E24
Continuity mistake: When Niles and Kit are at Frasier's apartment, Kit does a quick dance with her arms out and tells them Niles is taking her to Euro Disney. A couple of shots later her little purse is back under her arm, even though she had no time to pick it up from the bookcase.
Continuity mistake: Niles gets a pair of scissors to snip off a thread on his pants. He puts them on the ironing board, but after he passes out, they are on the credenza behind the couch. Later, they are back on the ironing board. (00:03:00 - 00:04:05)
Continuity mistake: Frasier gets out his address book to look for women he's dated but we can see the pages are blank even while he reads out names. He is not making them up, as he does phone one named Tatiana later.
How to Bury a Millionaire - S6-E7
Continuity mistake: Near the end of the show, Niles has signed his lease for the Shangra-La with his Noel Coward pen and he puts on the table next to the lease. A couple of shots later we can see the pen lying on top of the lease, even though no one touched it.
Continuity mistake: When Niles is engaged in his ironing fiasco, Eddie is watching his every move. When Niles heads to the kitchen to get spot remover, Eddie is sitting on the footstool. The next shot shows Eddie turned to watch Niles - but he is now in the chair; it is not just a tricky angle, as he actually lays his chin on the back of the chair. There was no time for Eddie to jump from the footstool to the chair.
Continuity mistake: At the end of the show, when Martin, Niles, and Frasier are leaving Niles's place to go out for ice cream, they leave Maris's opened package on a large footstool next to a decorative metal bowl. When they return (closing credits) with their ice cream the package and its wrappings are gone - even though no one was left behind in the apartment.
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.