Continuity mistake: In the conference room, Frasier says, "I just said that," and the shot shows his arms resting on the table with his hands up, gesturing. The next shot, from the side, shows him leaning back in his chair with his arms right off the table. The shot then goes back to the original position. There was no time for him to move naturally.
Continuity mistake: When Bulldog gets back to the kitchen table after closing the door on Roz's date Ted, there is a large blue casserole dish sitting there - it wasn't there when he went to answer the door. Roz had been hiding the whole time, so she didn't put it there.
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.
Continuity mistake: Niles says on Daphne's wedding day that he told her he loved her on his 3 day anniversary, making Daphne's wedding his 4 day anniversary. At Nervosa, Mel says it's their 4 day anniversary, when at this point one more night has passed and it's now 5 days since they married.
Continuity mistake: Frasier (and later the others) come back to his apartment to avoid the rain - they shake off umbrellas, and we even hear the storm at the very start of the scene. However there's no rain on the balcony - can't be covered, as we see in "call me irresponsible" during the obligatory sex scene that when it's raining the balcony gets soaked.
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.