Revealing mistake: You have to be very quick to spot this, but when the cannon goes off Niles drops the ring, you can actually see it drop between Eddie and the camera and bounce away from Eddie. In other words, it certainly doesn't go anywhere near the pate.David Mercier
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.
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: Frasier is on the phone at KACL with Jerome's girlfriend and the reflection in the glass shows him raising his hand to his face, but the next shot returns to him - his hand is on the console. There was no time for him to have shifted positions normally.
Visible crew/equipment: Towards the end of the show, Marty and Frasier are sitting in the living room talking. Eddie is curled up right next to Frasier on the couch. There are a number of shots focused on Frasier and Eddie and on the bottom of the screen one can see something flick by a couple of times - and in one shot there is definitely a couple of inches of a grey metal pole of some sort, about the thickness of a broom handle.
Other mistake: This is for the episode "Crock Tales" (the 22nd of the season). Almost all the flashback sequences are wrong in time. The one from 2003 has Niles and Daphne coming back from their honeymoon but they married in 2002. Although not ever couple take their honeymoon directly after they've married, the wedding episode "Ring Cycle" mentions them going on their honeymoon.
Continuity mistake: As part of his divorce settlement from Maris, Niles gains ownership of Shady Glen, Maris' mountain home. After this episode, Shady Glen is never seen or mentioned again. What's even odder is that Niles and the rest of the characters over the years go to mountain cabins, which makes no sense because wouldn't they just use Niles' place?
Continuity mistake: Daphne has the bag of groceries on the floor between the coffee table and the couch - when Stephanie leaves the apartment the loaf of bread is sticking out on the left side but when Marty comes into the living room, the bread is now on the other side of the bag and leaning to the right.