Revealing mistake: As the major tries to convince the Chief Inspector to leave the island, we see Hastings come down the stairs. However, prior to this we can see Hastings waiting just out of shot for his cue to enter. The edge of his hat is visible for several seconds, and when he's cued he begins walking into the shot. (01:15:27)
Agatha Christie's Poirot (1989)
1 revealing mistake in Evil Under the Sun - chronological order
Starring: David Suchet, Hugh Fraser, Philip Jackson, Pauline Moran
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.
Wasps' Nest - S3-E5
[Poirot is stung by a wasp]
Hercule Poirot: The open air! It should be closed during the summer! (00:18:40)
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?