Other mistake: Commissioner Selwyn Patterson puts some pressure on Humphrey and the team saying that "a wealthy tourist has just been killed." But Dan Hagen was not a tourist; he lived on Saint Marie with his wife, as said by the fellow oceanographer Jonathan Taylor, and they have a villa. Someone as well connected and nosy as Patterson wouldn't miss the notion of a multimillionaire living on the island. He also says that he needs to reassure the yacht club that there are no pirates in the area, but it was already established by the coast guard that no ships approached the area. (00:12:15)
Other mistake: Joséphine Jobert is a Sergeant (the commissioner introduces her as such at the end of the first episode), but in the end credits of all the episodes before she takes over for Camille Bordey and becomes officially a Detective Sergeant, she is merely credited as "Officer Florence Cassell." By comparison, Fidel was credited as "Sergeant Fidel Best", even not being a DS.
Other mistake: Florence closes her notepad and puts the cap back on the pen when Dwayne just begun telling everyone what the Gendarmerie reported about one of the suspects. She has no way to know by that point what Dwayne is about to disclose, and that Humphrey is about to leave with her. (00:17:05)
Episode #2.1 - S2-E1
Other mistake: Dwayne is a veteran police officer who's somehow never ever heard of Luminol (misspelled in close captions, incidentally). (00:14:30)
Episode #2.7 - S2-E7
Other mistake: The show, shot in Guadeloupe, part of France, is set in the fictional island of Saint Marie, British overseas territory, with English as official language. When we see the development company sign a big cheque to the local university, it is to the order of University of Guadeloupe (also non-existent, since the university in Guadeloupe would have been in 2012 the University of the French West Indies and Guiana). Incidentally, the document that supposedly incriminating picture (taken at an amazingly public event including giant cardboard fake cheque) is from, is a form about real estate in Nevada. (00:20:50)
Episode #2.2 - S2-E2
Other mistake: Sister Marguerite throughout the whole episode is wearing not very nun-like quantities of lipstick and mascara - especially considering that the head nun is depicted as strict and frowning upon things like chewing-gum.
Episode #1.3 - S1-E3
Other mistake: Investigating the crime scene, Richard, facing away from Camille, asks what was the victim drinking. Camille is already going for the glass of rum before he asks the question. (00:03:00)
I hope that watching the scene it can be clear. Camille was busy taking some notes, and he is facing away from her. All of a sudden, he says "So, what was she drinking?" and while he is at "So" Camille is literally lunging to her side to go look at the glass. Neither had any possible way to get that kind of timing, and it's not played as a "Hey, we were both thinking the same thing! Jinx!" kind of gag.
The Healer - S7-E4
Other mistake: The coroner report that mentions the nicotine poisoning has also as information in the first column that the victim came from the hospital with a suspected stab wound. That bit of information makes no sense and it's not mentioned in any way. Reused prop? (00:19:00)