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)
Episode list - season 1
Starring: David Suchet, Hugh Fraser, Philip Jackson, Pauline Moran
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)
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.
Question: Why does Poirot claim to be an American citizen when being interrogated by customs?
Answer: It sounds a bit like "American", but listen very closely and you will hear "Belgian".
Answer: He definitely says "Belgian", but the subtitles get it wrong and show him saying "American."
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