The Mysterious Affair at Styles - S3-E1
Continuity mistake: Hastings has just met the Ingelthorps, and now is outside so John Cavendish can introduce his wife. In the wide shot it's evident that John lowers his arm, but in the closer view his arm is still held up high before Mary speaks. (00:08:10)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: The first time Mrs. Ingelthorp is shown, she is holding a pen. In the second shot she is holding it in her right hand, while in the third she has the lid of the pen in the right hand and the pen itself in the left. (00:07:30)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Hastings receives the messages that he is wanted by someone outside the movie room; you can see the person sitting next to him turn towards him in the first shot, and re-turn towards him in the following. (00:02:25)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Everyone is silent at dinner after Miss Howard left, but Mr. Inglethorp keeps a healthy appetite. As he eats, look at his plate; the shadows cast on it switch side depending on the camera angle. (00:18:40)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Mary Cavendish's wine glass goes from almost empty to full and vice versa several times during the dinner scene the first day. (00:10:10 - 00:11:10)
The Adventure of the Western Star - S2-E9
Revealing mistake: Japp is waiting for Van Braks to make his move, and when he is hopping on a taxi for the airport, he begins to tail him. When the car moves, reflected in the door is a modern No Parking cone in bright yellow (incidentally, they also pass by a parked car with a FUU 692 plate that is a bit too recent for the series, being an Austin Big 7, first produced in 1937). (00:41:05)
The Adventure of the Western Star - S2-E9
Factual error: Assuming the episode is in line with the others of the season and it is set in 1935, a few vehicles shown are slightly too recent. The plane waiting for South Africa is a Beechcraft Model 18 (first produced in 1937), the train going to Yardly has a SR Q locomotor first produced in 1938, and the truck that slows Japp down before getting to the airport is a Bedford M-Type, a model first produced in 1939 (the specific one used in this episode is from 1947).
The Adventure of the Western Star - S2-E9
Continuity mistake: When Poirot enters the room of Mademoiselle Marvelle after her husband took off for the airport, she opens the door to him holding the door in two contrasting ways (right hand on the side of the door in the first shot, behind the door using the left hand to push it closed in the other). (00:41:35)
The Kidnapped Prime Minister - S2-E8
Factual error: The calendar behind Japp in Scotland Yard places November 13 as a Tuesday, but that is wrong for 1935, when the story is set (the whole season consistently goes with 1935 historical facts, Poirot in this episode makes a reference to "the Dutch", and the newspaper page Hastings shows up with at the end of the episode talks about the notorious gangster's death, happened that year). It was a Wednesday in 1935, to be Tuesday it should have been 1934. (00:34:00)
The Kidnapped Prime Minister - S2-E8
Factual error: At the end of the episode, during the fitting of the jacket with monsieur Fingler (last role of character actor Milo Sperber), Hastings is reading a newspaper prop sporting a doctored first page (the real headline, which was about Italy, is replaced by the fake PM speech) of The Daily Express based on the real Friday October 25th, 1935, which is wrong in month and day of the week (the appointment was on Thursday and it's supposed to be November going by the various calendars seen throughout the episode). (00:51:00)
The Kidnapped Prime Minister - S2-E8
Factual error: Poirot in this episode has to save the Prime Minister, kidnapped before he could attend the League of Nations Disarmament Conference. This episode is set in November (the previous of the season in October), but it can't possibly be 1935, since the Disarmament conference happened between 1932 and 1934. It makes mention of the PM being vital to have at least a chance at preventing Germany's rearmament, with Hitler withdrawing Germany from conference and League of Nations entirely in October 1933. It should be noted though that the conference happened in Geneva and not in Paris like it's described here. The original material did not have this sort of inconsistency since it was set to happen much earlier in the century and for the Treaty of Versailles, where Paris would have been the correct destination. Both short story and adaptation have as prime minister a fictional "David MacAdam", with him designed to be a stand-in for David Lloyd George, just recently replaced as PM.
The Adventure of the Cheap Flat - S2-E7
Plot hole: The professional hitman from the US does not have a gun of his own, and does not bother in the long time elapsed between the apartment's hit and the nightclub (it could even be hours) to check if the gun he just grabbed is loaded or not. Who in the world would not take a split second of his time to peek at the cylinder and see how many bullets does he have? An assassin planning to kill with that gun, even.
The Adventure of the Cheap Flat - S2-E7
Factual error: Agent Burt brushes off Poirot's question saying "When will you guys understand there is no such thing as the Mafia, the Black Hand or the Cosa Nostra?" The last term he uses, while not impossible (since members of the organization were indeed referring to it as such) is a huge improbability, considering that officially FBI (and certainly the general public Burt is lashing at) came to know the real name (adapted in "La cosa nostra") only decades later with the Valachi investigations. (00:24:05)
The Adventure of the Cheap Flat - S2-E7
Factual error: When Poirot asks O'Brian about unsolved crimes with young couples as suspects, he says "There's that Bonnie and Clyde of course, but they're at large somewhere in the American Midwest", to which Poirot replies "And let us hope that is where they remain." Bonnie and Clyde were killed in Louisiana on May 23, 1934. The episode is set in October 1935. (00:12:20)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: During the party, the establishing shot shows everyone in the small circle Poirot is a part of having a glass of champagne. That includes Mr. Robinson. As Poirot puts on the tray his own glass, someone's hand reaches over for another - it can only be Mr. Robinson's, as his wife is wearing gloves, but he never put down his own glass. (00:06:05)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Hastings, Japp (for some reason) and Poirot are at the movies; when the camera pans through the room, there's a guy sitting behind Hastings, while behind Poirot there are a red haired woman and a man, as confirmed by the close-ups. When the music stops and Hastings tells Poirot that he can open his eyes, the couple have moved behind Hastings. (00:02:50)
Double Sin - S2-E6
Continuity mistake: When Hastings storms out of the antique store claiming to have solved the case, Poirot follows him until he turns into an alley. In the view from the back of the alley, there's a man with a hat who walks all the way past Poirot and turns the corner into the main road. In the reverse angle, the guy is still walking down the alley in front of Poirot. (00:42:30)
Double Sin - S2-E6
Continuity mistake: Madame Durrant is showing the niece the medallions she is supposed to sell. In close-up you can see her holding the suspension ring with her right hand, and her left hand too, on the side, with the thumb on it. But in the wider shot, she is using merely the side and back of the left hand for support, the thumb being at distance from the jewel. (00:08:20)
Double Sin - S2-E6
Continuity mistake: Poirot has just been 'beastly' with Japp, in Hastings' words. In the establishing shot of the town square before the bus, a woman in orange (Miss Durant as we'll learn) pass by the ice cream cart. That same woman passes again the same spot as the camera is behind the cart, following the policeman and then getting Poirot and Hastings in frame. The driver and the man he was talking to are also in a different spot as that happens. (00:11:10)
The Disappearance of Mr. Davenheim - S2-E5
Plot hole: The killer has a perfect (in movie logic at least) plan but he amplifies its risks to 1000000% getting caught on purpose with an incriminating item that links him to his secret identity and that is amazingly likely to have him questioned and face the wife of the deceased (who recognizes him in 0.5 seconds) and other witnesses. Even without Poirot it is impossible to imagine a trial happening without him having to appear in some capacity. And in this TV dramatization, the motive of Lowen to hate Davenheim is obvious, but not the other way around, so it appears even more baffling that he'd utterly ruin his perfect escape just to mess with a rival apparently he had a upper hand on. Moreover, the dramatization makes his plan even more absurd, as instead of pawning the valuable ring like in the original and being only marginally involved, here he has it days after the murder, and robs the Inspector chief! Any bobby would do. Finally, here he also wears prosthetics, again drawing attention.