Continuity mistake: Frasier puts the tuna on the coffee table for Mr. Bottomsley and the cat jumps up and starts to eat it - he is facing the couch. In the next shot we see Eddie come into the room and suddenly the cat has moved and is facing Marty's chair - without enough time for the change.
Continuity mistake: Frederick is visiting and sitting on Frasier's couch with headphones on, playing a Gameboy. Frasier pulls off Freddy's headphones, which then lie around his neck while Frederick continues to hold the Gameboy. In the next shot, the headphones and Gameboy are on the coffee table and Freddy is sitting quite a bit to the left of them.
Continuity mistake: Frasier, Regan, Niles, and Poppy are at the ball - Frasier asks Regan to dance and she leaves her purse on the table, where we can see the strap hanging down over the edge. A couple of shots later, as they dance by, we can see the purse has changed position and the strap is lying on the table.
Continuity mistake: In the opening scene, Ronee and Frasier are talking at his table about her mother. Frasier asks, "She doesn't approve of premarital sex?" and his arm is folded in front of him. In the next shot, his elbow is on the table and his hand up in the air. Later on in the scene, Ronee's mother shows up at the door and we see Marty lunge to the right to grab his cane. A couple of seconds later the shot goes back to him and we see him lunge to the right for his cane again.
Continuity mistake: Across the show, Marty is supposed to be about 21 years older than Frasier (he turns 65 in season 5). There are at least two problems with his age - Frasier is supposed to have been born in March 1952 and in Season 5 (Roz and the Schnoz) Marty mentions going on shore leave as a single guy in 1952. Even if he was confused about the year, Frasier didn't call him on it. He must have done just a short stint in Korea as he was already a cop when he met Frasier's mother - they met at a murder scene, and he must have been 20 years old at the most. She was already a full fledged psychiatrist.