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.
Agatha Christie's Poirot (1989)
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Starring: David Suchet, Hugh Fraser, Philip Jackson, Pauline Moran
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An all-time classic, with the most impressive incarnation of the Belgian detective. If anything, because of the 25 years long commitment of the lead actor to his character, covering the entirety of the original stories and novels. There will be still many more versions of Poirot in movies and other media, each with a different take, but Suchet's work truly brought life to an icon most often identified just by his quirks and peculiar image, sort of a comic-relief magic gnome who solves inexplicable riddles. This is not what you get here, especially in the long run. Aging together with his character, Suchet (also executive producer in the latter stages of the series) brought gravitas and depth to this interpretation of Poirot, also thanks to a staggering amount of personal research, including some who may not resonate with everyone (such as Poirot's faith), but come from a respectful and thorough study of the source material. The scripts are solid dramatizations, and the direction is for the most part competent and hardly groundbreaking, but it will live on as a memorable act of love towards a literary creation.
More mistakes in Agatha Christie's Poirot
The Tragedy at Marsdon Manor - S3-E6
Samuel Naughton: Was the accomodation all right?
Hercule Poirot: No, monsieur Naughton. The accomodation was all wrong.
Samuel Naughton: Oh...
Hercule Poirot: The duck-feather pillows. It feels as if the duck are still in them. (00:14:50)
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?