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: 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: 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: 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)
Other mistake: In the bank statement that Dwayne hands to the DI, there are cash withdrawals "from the past three months", with the past three months being January, February and...February, again. (00:20:30)
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)
Character mistake: Florence says that Commissioner Selwyn Patterson and Martha are halfway through the bottle, but the bottle is practically empty. (00:29:55)
Other mistake: Torey Martin says that he had an accident 5 months before, but the car crash evaluation is signed 31/07/2016. Not only it was a Sunday - unlikely day for the car shop to be working -, but that would put the events of the episode on January, contradicting the bank statements and what was established in previous episodes.
Plot hole: The big climax of the episode involves Humphrey arriving at 1 PM to escort Martha to the airport as he promised, finding the shack empty with a parting letter from her and rushing on Dwayne's motorbike to catch her plane, failing to do so. All very cinematic, but that means that had Martha not left early, she could have not caught the plane at all.
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: 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)
Other mistake: The police boat approaches the scenes of the crime coming in from the right, in a straight line, then in the proximity of the boat they turn around it, moving clockwise, passing in front of the bow and then to the left side. When they review the readings though, the icons show a completely different story, as if the police boat approached from behind and they boarded docking right at the stern. (00:04:40 - 00:08:00)
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: 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)
Revealing mistake: Dwayne turns the volume of the computer in DI Jack Mooney's office; when we start hear him, the volume has gone up just a few notches, but it's already just as loud in the end as it is when Dwayne finishes to set it. (00:29:10)
Continuity mistake: Humphrey picks up the folders of the suspects from Mooney's desk using his left hand, and in the next shot they are in his right hand. (00:31:10)
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: 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: 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)
Revealing mistake: The photo found by JP in the newspaper archive is photoshopped so badly that you can actually see the line where Julian Wadham's face has been pasted onto the sailor's head. (00:44:55)
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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