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.
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.
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 is at Daphne's shower, saying "God, he sounds just like a prince," in reference to Simon - in her left hand is a drink and her right hand is positioned down, as though it is in her pocket. In the next shot she is still holding her drink in her left hand, but is giving Daphne a drink with her right hand - it just appears out of nowhere.
Continuity mistake: Early on in the show, Frasier and Martin are having breakfast and we can see an orange napkin in Marty's lap. While he is talking, the camera angle behind his shoulder shows his left hand against his cheek. Right after that the napkin appears on the table to the left - with no time for him to have moved his hand and put it there.
Revealing mistake: When Reagan drops her bag in the hallway when she is talking to Frasier, a lettuce rolls towards him. It didn't fall from her bag: if you look closely you can see it was tossed into the frame from just outside the camera view, obviously to ensure that it would land at Frasier's feet for the comic effect of him kicking it back to her.
Continuity mistake: During the opening credits, Frasier, Martin, and Daphne are sitting at the table talking about getting older. At one point Martin says "when people reach our stage in life" and his left hand is holding his coffee cup. But as the camera cuts to Frasier we can see Martin's hand in the left corner of the screen, up in the air, without the cup. The next shot shows it back on the table, holding the cup again. All this happens too quickly for the changes in real time.