Continuity mistake: During breakfast, there is a bowl of scrambled egg next to Martin that moves itself around, and at one point the fork in it just vanishes and then reappears.
Continuity mistake: As Marty says "Claire says", he is holding his sandwich is both hands. As Daphne turns towards him and says "shut up", he is holding the sandwich in his left hand and his right hand is on the arm of his chair. There was no time for the switch.
Continuity mistake: Near the beginning of the show, Daphne is having a smoke, and Frasier takes it from her - her hand is on her knee but when the shot changes it is in her lap.
The Bad Son - S8-E3
Continuity mistake: Frasier and Roz are on the bus, holding on to a pole; Roz has her purse on her right shoulder. As they talk about Miranda, her purse switches to her left shoulder and then back to her right, without her ever adjusting it.
Adventures in Paradise (1) - S2-E8
Continuity mistake: When Frasier comes into the living room, Marty's cigar box is open. The shot then shows Frasier talking to Eddie about his socks, and the cigar box is suddenly closed. At the end of the scene, the cigar box is open again.
Duke's, We Hardly Knew You - S2-E5
Continuity mistake: Near the end of the show, when Niles, Frasier, and Martin are at Duke's, Niles says, "I'm not here just for you, Dad" and he puts his hand on Marty's shoulder. The next shot shows him standing about two feet away, with his hands by his side. (00:21:20)
Flour Child - S2-E4
Continuity mistake: Arleen the cab driver is in labour. She pushes her hair back with her hand in one shot, but in the next it is back on the steering wheel, without enough time for this to happen in real time. (00:05:50)
Sleeping with the Enemy - S3-E6
Continuity mistake: Roz is talking about confronting Kate and says "you're damn right we're going to tell her", her arms go from being folded in front of her to down by her sides with no time for this to happen naturally.
Continuity mistake: Frasier is sitting on his couch with Poppy, dropping hints about having an arts show on KACL - she has her hands folded on her knee. As Daphne says "he means your mother", the shot changes, and Poppy is suddenly holding a glass of wine, with no time for this to have happened.
Kisses Sweeter Than Wine - S3-E5
Continuity mistake: When Niles first takes out a hanky to put to his bleeding nose, it is folded in a square and remains that way for a couple of shots. Soon, though, without Niles changing it, the hanky becomes rectangular.
Continuity mistake: While talking to Niles at the party, Daphne's eyes are tearing because of an allergy. In one shot we see her put a tissue to her right eye, but the next shot shows her dabbing it to her left eye.
Radio Wars - S7-E3
Continuity mistake: Similar errors occur in two different scenes: in the first breakfast scene, the coffee pot is sitting on the table but in the next shot Daphne is pouring herself a cup, with no time for her to have naturally picked it up. Later in another scene, Niles is there for breakfast, picks up the pot, and pours himself some coffee. In the next shot, the pot is on the table, again without enough time for him to have put it back.
Plot hole: Once the gang have arrived in Canada, Daphne is scared stiff of getting caught outside the USA. Marty explains they will just "smuggle" her back and Frasier and Niles are outraged at such deception. But to get into Canada, all of them would have had to declare their residence, birthplace, and reason for coming in. To get Daphne in in the first place, they must have lied. She would have had to show her passport as an alien. The Americans would have been allowed in without their passports, per diplomatic agreements. So the outrage of the boys makes no sense.
Other mistake: When Frasier enters the apartment, Martin and Sherry are talking in the kitchen. If you listen carefully to what they're saying, their conversation makes no sense. Martin says something along the lines of "Daphne is really a very nice girl" before suddenly, in a very different tone of voice, he says "You're right, we're not getting enough privacy around here". Seems like a big chunk of conversation was edited out.
And the Whimper is... - S1-E18
Continuity mistake: When Roz and Frasier are sitting on the couch discussing how the other award nominees are courting the judges, the amount of champagne in Frasier's glass goes down dramatically without him drinking any.
Continuity mistake: Roz goes to Frasier's to tell him Luke has been seeing someone else - while they are drinking in the kitchen, the level of her drink changes without her drinking or having a refill.
Revealing mistake: I think there might be something wrong with the eels in this episode. They don't move in the tank, despite being alive and don't move when taken out either. Moreover, you cannot actually see any in the tank with one exception. Rubber replacements not up to standard obviously.
Continuity mistake: When Frasier is talking to Patrick Stewart (who is putting his coat on) in Cafe Nervosa, the collar on Patrick's coat fixes itself between shots, without him doing anything to it. In particular, one of the lapels is stuck under the coat for one shot and is suddenly normal in the next shot.
Audio problem: As Frasier walks into Niles' kitchen, Daphne is on the phone, talking. We hear a hoarse sound, like Frasier's voice, saying "Daph" or "Dad" but it makes no sense as she is on the phone talking to someone, and he is heading for the fridge. When she hangs up, she and Frasier start talking about her employment situation.
Miracle on Third or Fourth Street - S1-E12
Continuity mistake: Early in the show Frasier is wrapping a Xmas present for Roz. The shot cuts to Chopper Dave and then back to Frasier. A bow and gift tag have appeared on the gift, but there wasn't enough time for that to have happened naturally.
Answer: It equals the record of James Arness of "Gunsmoke" for the actor who's played the same part on TV NOT in a soap opera. If you include soaps there are two main contenders - William Roache, who's been playing Ken Barlow in "Coronation Street" in the UK since 1960. Don Hastings has been playing Robert Hughes in US soap "As the World Turns" since 1960 as well.