Episode #1.1 - S1-E1
Plot hole: The real culprit pinned the crime on DI Charlie Hulme, but since everything was improvised and acted on the spot, it doesn't explain how could they access Charlie's safety deposit box at the bank stuffing it with incriminating evidence. It is specified through Fidel and Dwayne's dialogue that the box is at the bank, where everyone is required to show identification to get a box and access it, not some anonymous private storage company or a random locker.
Suggested correction: Since the murderer is with the police, it's possible she found a way to convince the bank clerk to allow her access. But unless the clerk was in on it and manipulated the record or such, it should have come out immediately when Poole investigated the locker. Hard to believe he wouldn't ask about the last access.
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.
