Continuity mistake: Near the beginning of the show, Frasier brings Roz a muffin in a bag which she places to the left of her phone (her left). During the scene, the bag shifts from being near the console to being back to left of the phone. At one point Frasier and Roz leave the booth, then come back in, and it has moved in the meantime.
Continuity mistake: Frasier and Martin are in the kitchen and Marty gets some chips out of the cupboard next to the fridge. As he leans down to pet Eddie we can see a bag of blue chips still in the cupboard - but when he straightens up to talk to Frasier, we see a red bag in the cupboard, not the blue one (the camera angle remains the same).
Continuity mistake: Frasier is sitting on the couch watching Wheel of Fortune and eating, with a plate on his stomach. As he talks to Niles he places the plate on the coffee table. Niles says "Are those profiteroles?" and Frasier gobbles them up. Then we see Frasier put the plate on the table again.
Continuity mistake: In the opening scene, Roz and Frasier are in Cafe Nervosa, and she is snoozing, while a half-eaten muffin sits in front her. As she wakes up and talks to Frasier, the muffin appears whole again. She leaves and Martin comes in and takes her seat. A shot then shows the muffin as half-eaten again, even though no one has touched it.
Plot hole: Niles phones Frasier to tell him Daphne is staying at his place because of the storm. Frasier's phone is in its usual place on the room divider/bookcase behind Marty's chair. After Frasier and Marty leave to rescue Daphne, Niles phones again and Eddie is standing up on a chair staring at the phone. Only problem is, the phone is over on Frasier's desk, where there normally is no phone. If he did have a phone there, it is only a few feet from the other one, which makes no sense.
Continuity mistake: During the first episode of Frasier there is a painting of some vases in Frasier's apartment which is at the end of the hall leading on to Daphne's room. In this episode the painting has a red and purple background, however in 'Here's looking at you' (S1, 2 mins 52 secs) the exact same painting is now red and blue. It remains this new colour for the entire 11 seasons.
Plot hole: Niles makes up Frasier's couch to sleep in and when he lies down he lets out a yelp - and pulls a plastic pirate's hook from behind the cushions. Earlier Niles had appeared wearing a pirate's costume but at no point did he have a hook, nor did he go near the couch. His overcoat had been on the floor the whole time so it couldn't have come from there. It would have been difficult for it to get behind the cushions unless deliberately shoved there, which we never saw and makes no sense anyway.
Revealing mistake: About 1/3 through the episode, they are in Roz's apartment. If you watch when people enter or leave the apartment, the door has a handle lockset. It also has a lock cylinder about 1 1/2 feet above it on both sides of the door. The problem is, the side of the door has no drill hole where the latch assembly should be: it's just solid wood. The lock isn't attached to anything that would enable it to work.
Revealing mistake: In the scene where Frasier and Lilith meet in the living room, where Frederick has created a romantic atmosphere, Frasier has a long speech about how Lilith is not going to get him back, ending with "I need to be finessed!" and Bebe Neuwirth goes out of character and begins to giggle, before she quickly covers her mouth and pulls herself together. Though Lilith might have found Frasier's comment amusing, it would definitely not be in character for her to giggle like that.
Continuity mistake: Roz comes back to the restaurant table, after phoning her babysitter, and says, "I have to go". At this point her purse is over her wrist. As she finishes saying, "Alice got a bead up her nose", she is holding the purse by its strap. A few shots later it is over her wrist again, even though she never moved it.
Continuity mistake: When Luke and Frasier are talking in the restaurant, and Frasier asks, "So Luke, you're a boat enthusiast?", his forearm is resting on the table. When the shot cuts back to him, only his hand is resting on the table, with no time for him to change position.
Continuity mistake: When Sherry brings in the bottle of wine, it's in a paper bag which is twisted around the bottle when she puts it on the coffee table. The next shot shows the bag has been loosened around the bottle and is quite wrinkled. No one touched it in that short time.
Continuity mistake: Frasier is just saying goodbye to Niles and we can see the brochure for Daphne's reception to the left of his sherry glass. When he stands up and shouts "Daphne!" the brochure has moved about 6 inches to the right, even though no one touched it.