Continuity mistake: JP is interviewing the widow. When she is reacting to the latest questions, her hand is open in the frontals, closed in the rear views. (00:37:00)
Continuity mistake: Jack tells the silly story of his cuff-collecting, one-armed uncle; in the reaction shot, Humphrey is sitting with his left arm up in a recognizable position, which changes in the next shot. (00:35:40)
Continuity mistake: Jack sits at the conference table, next to Florence. She moves the hand away from the notepad, but it's back on it at the cut. (00:34:20)
Continuity mistake: In the Scotland Yard office, DI Humphrey Goodman turns around and finds the teleconferencing DI Jack Mooney on screen. He announces to the team "I think I may have found him", and turns around, holding the phone closer to his chest. The movement is repeated in the next shot. (00:28:50)
Continuity mistake: A business card from CityMet Bank comes into play. Humphrey points at the whiteboard with the card, but in the next shot the card becomes a magic marker. (00:23:00)
Continuity mistake: Humphrey passes the bridge and meets by chance the distressed ginger; when he startles her, the phone instantaneously switches from right to left hand. (00:03:40)
Continuity mistake: During Dwayne's annual appraisal, Humphrey holds a bic pen that faces different directions in the reverse shots (easy to tell from the cap being on opposite sides). At the end of it he removes his hand from the desk, but it is back at the middle of the questionnaire in the next shot. (00:00:50)
Continuity mistake: Evening at Humphrey's; Goodman and the two French main characters are looking at the unlikely pair of the Commissioner and Martha being drinking buddies. Florence is looking over her left shoulder in a pinup pose, but she is turned right in the reverse shot. (00:29:45)
Continuity mistake: Goodman rushes out of the police station after spying someone tampering with the jeep. First time we see the various market stalls in front of the station, and two women are moving from one stall to another; one of them is wearing a sleeveless pink dress and has her hair in a bun. Humphrey arrives by the jeep in the next shot, and the two are back to the same stall they departed from earlier. (00:17:35)
Continuity mistake: This is one of those episodes where names of the suspects on the whiteboard they look different under different angles. The horizontal stroke of the J in "Jerome Martin" is touching the hook, or not, the B in "Sabrina Martin" is different, etc. (00:13:15)
Continuity mistake: Florence spots the camera inside the cricket club's bar and points at it as she goes to fetch it. Points with her right hand, becoming the left hand at the cut. (00:11:20)
Continuity mistake: Opening; a creepy dude puts his hand on the shoulder of the hero of the cricket game. In close-ups the hand is not on the polo's neck, in the intermediate wide shot it is right on it. (00:02:55)
Continuity mistake: Dwayne answers to Humphrey about his splinter in a close-up. His hands are at a very much different distance than in the previous shot. (00:36:35)
Continuity mistake: While Florence is going through the humanitarian career choices of the victim with Humprey, Dwayne is having a phone conversation with the secretary of the solicitor (somehow not being disturbed by the others speaking loudly, and conveniently being heard only when he says bye). Next to him, there's a biro pen at the side of a notepad. Change of angle, and the pen is on top of the pad, and then again to the side of it. (00:24:45)
Continuity mistake: When Humphrey puts the ancient cigarette packet under Dwayne's nose, his hand is on the top, bottom, top corner. (00:20:55)
Continuity mistake: Dwayne passes Humphrey the bagged notepad with a UK phone number scribbled on it. In close-up he is holding it with one hand. In the next shot his lips are still moving and yet he is holding it with two hands. (00:17:10)
Continuity mistake: Florence hands to her boss the freshly printed picture of Elliot Taylor using opposite hands in the shot and its reverse. (00:15:30)
Continuity mistake: At the end of the first interview with the suspects, Florence caps Humprey's thank you to the helpful staffers with a rather unsubtle eyeroll. She changes position lowering the pen, that is on the other side and higher in the following shot, last of the scene. (00:15:00)
Continuity mistake: DI Humphrey Goodman debriefed his team who just arrived on the island, and is about to head out to interview the staff. Elliot Taylor passes a glass to his wife, who picks it with her right hand and places it down on the armrest with the same hand, the other one holding a bottle of medicine. Next shot, and the hands swapped contents. (00:12:20)
Continuity mistake: Humphrey tries to sneak away without waking Martha up, but being Humphrey he fails. In the shot when he stands back up after the hilarious bawl, the bed is sunlit, contradicting what is shown before and after. (00:10:10)
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.
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