The Kidnapped Prime Minister - S2-E8
Stupidity: In the episode, Hastings stalks Mrs. Daniels, being parked for hours literally in front of her windows, and the army surrounds the destroyed family mansion 'hiding' behind bushes totally visible, not scattered and standing in a way that makes them perfect targets. Nobody knows the first thing about secrecy.
Stupidity: The policemen in car 7 are able to take pictures and talk to Japp with total ease, with a direct eyeline at such a low distance from the 3 people that is quite amazing they haven't been discovered - everyone was blind and possibly deaf, since they were so close and with the window open, you'd think they could even easily be heard.
Stupidity: The gang is brutal enough to have Lavington killed; considering they know where he lives and that there's just a single housekeeper, it would have been miles easier for them to just kill or tie her up and ransack the house themselves with all the time they wanted, rather than involving the most famous detective with an obvious ruse and hope he'd find the object.
Stupidity: Radnor lives in the small village, Hastings does not. It's a miracle that his bluff worked, since the random two guys downstairs could have very well been two villagers he didn't meet during the couple days he's been there a month before, but that Radnor knows.
Double Sin - S2-E6
Stupidity: How in the world did Miss Lemon spend 2 days (and nights!) in the office searching for the keys but without looking on the console right next to the door? (00:40:25)
Stupidity: As far as I can tell this is not a problem introduced by the novelization, but already coming from the original story: without Poirot's involvement, called upon by the murderer, the police would not have suspected murder at all, and still would have a witness with a rock solid alibi to talk about The Dream. If they really wanted another witness, they could and should have summoned a psychiatrist and do to them the same stage act they did with Poirot, they would have been much more qualified witnesses to frame it as suicide. Even to Poirot himself, it's the murderer who suggests the thought there could be foul play involved, at all! The plan makes zero sense because Poirot is not the ideal witness and they want to suggest the victim was mentally ill and suicidal, not that someone wanted to kill him.
Stupidity: Hard to swallow that a group of vastly experienced policemen smart enough to figure other tricks out (such as the abnormal position of the gun) would be in any doubt about the victim being left or right handed when she is still wearing their watch on the right wrist - and attention is called by Poirot upon that particular detail right from the start.
Answer: He definitely says "Belgian", but the subtitles get it wrong and show him saying "American."
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