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: Mel and Niles are sitting on the couch at Frasier's. She is very upset and starts to open her purse for a hanky. In one shot she is fumbling with her purse and in the next the hanky is already in her hand - and not enough time to have done this naturally.
Continuity mistake: Frasier goes to get a newspaper out of the curbside kiosk, and catches his jacket in it. He places the newspaper to his right on top of the rack beside it and the shot changes to Regan coming out of the florist behind him. Then we see the newspaper in his left hand, without having time to have picked it up.
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.
Continuity mistake: Frasier and Roz are in Cafe Nervosa and Roz is looking at a newspaper while Frasier talks about giving Donny a bachelor party. Roz puts the paper in her lap, but in the next shot over her shoulder we can see that she is still holding the paper up.
Continuity mistake: Niles comes into Cafe Nervosa holding a newspaper and begins to talk to Frasier and Roz. As he says "mere words cannot", the shot changes and the next shot shows the newspaper has flipped over to the other side in his hand. He didn't have time to do this naturally.