Plot hole: Hastings came over to assist Poirot in his case, posting guard overnight. He offers to drive Poirot back to the villa since Poirot is in a rush and has figured out of the culprit. Poirot approaches the villa just in time to come across Mrs. Vanderlyn on her way out. Poirot rushes to Hastings then to give chase to the woman but...Hastings has pulled out all the plugs and is cleaning the carburettor, just doing some random maintenance to the car that would take him, in his words "an hour" to bring back to work. On a one-day job, Hastings crippled their own car for no reason whatsoever. This is beyond stupidity.

Agatha Christie's Poirot (1989)
1 plot hole in The Incredible Theft - chronological order
Starring: David Suchet, Hugh Fraser, Philip Jackson, Pauline Moran
The Mysterious Affair at Styles - S3-E1
Plot hole: Can't fault this massive plot hole to the adaptation, but to the source material; the culprit (forgetting the stupidity of writing an incriminating letter detailing the plan to murder someone, and put it in a desk he shares with her) since there are people outside the room that are about to enter, tears the letter in 3 neat vertical strips, rolls them, puts them in the vase on the mantlepiece, and then opens the side door to slip away...instead of simply pocketing the letter and going through that same door. Nobody was going to search him or anything and could have burned it, torn it into confetti, anything, later. It takes way way longer to do what he did, which needed him to stay there in the room increasing the chances of being found out. And of course he and his accomplice do not retrieve the letter after.
The Disappearance of Mr. Davenheim - S2-E5
Hercule Poirot: And please, do not fraternize with that creature. I am still training him.
Captain Hastings: It's only a parrot.
Hercule Poirot: I was talking to the parrot. (00:27:00)
Trivia: Poirot in the ship's lounge is reading the actual May 1st 1935 issue of Bystander (recognizable by the cover and with the correct page order, does not seem to be a simple movie prop), roughly consistent with the time frame of the first season and a contest taking place on the 14th. (00:07:50)
The Murder of Roger Ackroyd - S7-E1
Question: The doctor (James) put on a Dictaphone to make the suggestion that Roger Ackroyd was alive at 21:30 hrs. But how could he know that someone (Paton) would pass the door of Ackroyd's study at precisely that moment?
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