These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Critical Research Failure: In Death in the Clouds, it is said that a blowpipe is about a foot long, when in actuality it is six feet long, a mistake that Christie admitted. Ariadne Oliver also makes a reference to the research failure in a novel of hers in Mrs. McGinty's Dead.
"Funny Aneurysm" Moment: The short story "The Kidnapped Prime Minister", set in 1919 and written in 1925, is about Poirot having to find the titular kidnapped Prime Minister before the Versailles negotiations start, because if he is not present then the treaty might be 'too lenient'. Of course in hindsight it's generally thought now that the harshness of the Versailles treaty played a major role in the rise of Adolf Hitler.
Readers in Mourning: Poirot is the only fictional character to receive an obituary in the New York Times. Although, at least one paper did an obit for Chewbacca.
Recycled Script: Some of Poirot's adventures are so good, other characters copy them.
Values Dissonance: "The Augean Stables" sees Poirot go to great lengths to bury and discredit accusations of embezzlement by a former Prime Minister... which happen to be true. This obstruction of justice, which involves destroying a man's career, is considered right and proper in order to defend the late Prime Minister's reputation, prevent his party from suffering a great loss of face, and prevent a politician from another party from becoming the new Prime Minister (as he is considered to be most unsuitable for the position). Nowadays Poirot would be the villain in the story. Although to be fair, Poirot says he would not lift a finger were the politician still alive, and that Don't Shoot the Message is the only reason he's getting involved at all.