Other mistake: Inevitably the officers have to concisely give to the quirky inspector a quick profile of the suspect. For their "background checks" they read from profile sheets. It is unclear if they wrote them themselves or not; sometimes especially in earlier seasons they seem to receive them. These sheets contain sentences often written in a rather informal tone that does not fit the format, and in fact often you can see that whatever the officer is saying in casual tone as if it were part of the dialogue is written verbatim on the sheet itself. Example; 6-8, when Florence says "He's big on family values and promoting education in the community", with her line already readable word for word on the sheet in Jack's hand in the previous shot.
Death in Paradise (2011)
1 other mistake in show generally - chronological order
Episode #1.5 - S1-E5
Plot hole: Leon Hamilton is the most hated man in Sainte Marie, with over 900 people on the island conned by him. Yet exactly one person in the whole island knows how he looks like, every newspaper and website never ever published a picture of him even during the very public trial when they were trying to get their thousands of dollars back nor publish an archive picture after his death.
DI Jack Mooney: Strictly speaking, paradise is a state of mind. You know that, right? I mean, the dung beetle - very different idea of paradise, doesn't he? (00:48:25)
In the Footsteps of a Killer - S6-E7
Trivia: In the close-up of the diary of Julie Matlock, you can read in the column to the right of the page with the mysterious number 19871 a name; Agnes Dahan. It's the name of the production buyer of the episode, and long time staff member of the show in production and art department. (00:20:20)
Question: Why don't they even think of pretending the victim just drunkenly tripped in the kitchen while getting a sandwich, and his sister-in-law reflexively tried to catch him, unfortunately holding a knife? He thought he would live a few more minutes, so he could have backed up the story. Instead, everybody (victim and police) just takes it as given that the stabbing will reveal their relationship.