Continuity mistake: Right at the start when Frasier is talking to Niles in the furniture shop, at one point he says "Don't you hear that," and holds his hand in a fist. The shot cuts instantly to Niles and you can see his hand is now about a foot higher and his palm is suddenly open.
Continuity mistake: Martin goes out to a baseball game with a famous writer that Frasier and Niles admire. While he is out, they read one of his books he accidentally left behind. When the author returns, he ends up holding the pages of the book in his hand, whilst standing in front of the fireplace. In one shot he is holding them in his left hand, but when the view cuts to another angle, he has them in his right hand. This occurs just before he goes outside to throw the pages off the balcony.
Continuity mistake: Daphne is on the phone with her mother and has a dust rag in her hand. She holds out the phone towards Frasier and when the shot goes back to her, the rag is all bunched up in her hand - it has been loose before. There was no time for her to change it.
Continuity mistake: Frasier, Martin, Niles, Daphne, and Diane are having dinner at Frasier's and he gets up to get dessert. Niles offers to help him and puts his table napkin in his chair. As he walks towards the kitchen, though, the napkin is lying next to his plate.
Continuity mistake: Marty gives Niles a mug which says "World's Greatest Psychiatrist." He puts it down on the coffee table with the lettering facing the camera. He then leaves with Daphne and a few shots later, we can see the mug again, but it is turned around and we see the blank side. When Frasier leaves the apartment, it's back in its original position. Nobody ever touched it.
Continuity mistake: When Daphne is playing darts with Frasier, he says, "I scored again," and we see her sweater sleeve is pushed up her arm. But when she comes back with, "That's not something we hear very often," the sleeve is completely covering her arm. In the next shot, it's pushed up her arm again. There was no time for the adjustment.
Continuity mistake: Roz is at Frasier's to tape some CDs, and we see her take some cassettes out of her purse. The shot goes to Frasier and then back to her - the cassettes have disappeared. After he explains that he can't stay, we see Roz open her purse and take out the cassettes again.
Continuity mistake: As Frasier tells Bulldog that he shouldn't feel threatened by Clint, we can see the edge of a clipboard moving on the bottom right screen, where Roz would be. However, in the shot before that, Roz had pretended to punch Bulldog - she had nothing in her hand and wouldn't have had time to pick anything up.
Continuity mistake: At the beginning of the show, Frasier is sitting with Martin and Niles in Cafe Nervosa telling them about the radio play. As Marty says "we were a simple people", Frasier manages to open his briefcase, take out the script, put it on the table, and put his briefcase back on the floor and be sitting still - all in about 3 seconds. This just wouldn't be possible in real time.