Continuity mistake: The detectives reach Cressida Friend on the beach. Jack waves around the letters with his right hand; his left hand is in his pocket in the front views, but it's on the waist in the wider shot. (00:32:00)
Other mistake: According to his passport, Michael Bennett was born on July 120th. (00:35:50)
Continuity mistake: At the harbour, Florence's ponytail is suddenly windblown in the shot when Jack says "I'd say that gives you a pretty good reason to want revenge." (00:37:15)
Continuity mistake: Officer J.P. Hooper holds the wad of bills for an unnaturally long amount of time, but if it was for sake of continuity, too bad; he holds it with his arm at a different angle between shots (he did not have his elbow on the desk, and all of a sudden he does). (00:37:20)
Plot hole: The way Jack narrates the murder does not make sense; according to him, the killer went first to grab the telephone, then back to the garden to kill the victim, then from there, he had to go, unnoticed and with his robe loose, back to the shack (which seems to be close to the entrance and the box where the phone was). Moreover, to stick the rope into the clay sculpture, especially the way we see it, not entwined into a ball but unfurled, he needed to disrupt the sculpture in a way that would have been noticeable, even if the clay was not entirely dry yet.
Plot hole: One of the guests is a journalist going undercover. The police finds him out because...they google his name, "Bryn Williams journalist" (no quotation marks), but then not finding anything (and Jack says so despite actual results being visualized, but he dismisses them at a glance) Florence has a stroke of genius and says "William Bryn then." And this time the googling pays off, with a search result page that says, literally, that he's an investigative journalist "known for going undercover to investigate", apparently being a master at that having won prizes! In all this amazing silliness, it appears quite impossible that they wouldn't know his real name, since they already identified the suspects and ran background checks, which in every episode always include checking with immigration when they entered Saint Marie. He couldn't have entered the country under a fake name.
Continuity mistake: Florence at the beginning of the episode dismounts from the police Defender putting her right hand on the inside handle of the door, but she has her fingers at the top of the open window in the next shot. (00:03:40)
Continuity mistake: Crouched by the victim, Florence points out of the most likely murder weapon. Between shots she changes position on the floor, as easily shown by the large tiles on the floor; sometimes she has both feet on the same one close to the statue, other times she does not. (00:05:15)
Continuity mistake: In his initial reconstruction of the struggle, Jack says."falls to the floor just here." JP has his hat in hand on the left side of his body. Then Jack continues "and then crawls forward", with no pause. In this new shot, JP's hat is on the right side and he in a totally different posture. (00:05:45)
Continuity mistake: When Jack declares that the case is "Still firmly open", JP has his hand above the belt, but his hand is down past the hip in the next shot. In the rest of the scene his arm position keeps being inconsistent; he has them open to different heights and°. (00:12:10)
Continuity mistake: At the station, when Jack holds the bag with the lone peanut, the bag is in a completely different position between shots. (00:13:40)
Continuity mistake: When Jack says "I am so sorry, Dwayne" telling him to go to the birthday dinner, he repeats in the two separate shots the same gesture, hand starting from a different spot at each cut. (00:31:55)
Continuity mistake: When Jack shows the peanut to the 4 suspects, the legume is in a different part of the bag each time without him moving the bag. (00:45:25)
Continuity mistake: At the beginning of the denouement, Jack is holding the statuette; he holds it by the bottom or upturned depending on the camera angle. (00:45:35)
Continuity mistake: When JP and Cordell Thomas toast at the end of the episode, the obligatory bottle of Etensel in JP's hand is facing the opposite way between shots. (00:50:45)
Continuity mistake: Getting to celebrate at the end of the episode, Dwayne is chewing on some ribs, but in the reverse shot Darlene is reacting to him eating from a fork in the foreground. He puts down the same rib later when she has to get up to answer the door. (00:50:55)
Other mistake: The victim is said to have died between 10 and 11 but the neighbour put his bins out at midnight and heard the fight.
Plot hole: At the beginning of the episode it is established that Samuel Palmer "was putting out his rubbish just after midnight", but in the rest of the case (coroner report, case discussion at the station, question to the suspects) the time of death is 10 PM. The part of the dialogue at the beginning (Dwayne talking to Jack and Florence outside the house) is cut in home video releases, but still appears in Jack's case-solving flashback reel. Other references to the wrong midnight time appear in Cordell' statement as he turns himself in (says he entered from the window " Just before midnight.") and Jack's usual schtick with the suspects ("Shortly after midnight, Eugene's neighbour, Samuel, he heard arguing").
Continuity mistake: It's a locked room mystery, and to make it more obvious the pretty aide asks how was it possible for the killer to do it. Jack answers "There's the rub, Florence"; viewed from behind, Jack has both hands on the handkerchief, but from the front, just one. (00:04:35)
Continuity mistake: When Jack picks up the fork from the floor, it keeps turning around in the first couple of shots and in the last couple of shots (when Florence goes to talk to the others). (00:04:45)
Answer: There's probably no particular reason. Sets and props on long-running TV shows often change as needed and for various reasons throughout a series run.
raywest ★