Agatha Christie's Poirot (1989)

Peril at End House - S2-E1

Plot hole: The hole in the hat was pre-existing and the bullet was fired in advance and dropped. Poirot notices immediately the hole when Nick puts the hat down but somehow missed it while she was wearing it as she supported him. He also does not notice that the bullet has not been fired at that time - which would have been still hot if just fired, not at all if dropped. Most importantly, in the spot where they were sitting, it's not even possible to think where a shooter could have ever been hidden; nobody wonders where the mysterious shooter could have been or cares to investigate the circumstance despite knowing the very moment the supposed shot happened. The fact is basically ignored throughout the rest of the episode.

Sammo ★

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)

Sammo ★

The Disappearance of Mr. Davenheim - S2-E5

Trivia: David Suchet performed all the various conjuring tricks Poirot is trying to pull off. The illusionist in the theater show at the beginning is the late Patrick Page, real life stage magician and coach/consultant for the episode.

Sammo ★

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?