Continuity mistake: Mrs Pengelley is outraged by Hastings' question about the niece. Poirot opens his umbrella and begins to move forward to ask a different question. The left side of his coat is mostly spotless, but in the next close-up that side is instead covered in water stains, including a quite visible streak on the chest. (00:05:40)
Factual error: One of the two police cars identified as Unit 10, is appropriately enough, a Sunbeam-Talbot Ten. The episode is set in 1935 though (with amazing accuracy for some details, including the poster for the movie "George White's Scandals 1935" shown before the car tailing starts), and that car was manufactured only after 1937. (00:19:55 - 00:22:00)
Other mistake: Japp manages to coordinate the pincer action of the 3 police cars using a very broad map and no real information about the whereabouts of the suspect. The whole scene is rather silly, it would work in a modern thriller with a GPS, perhaps, not with toy cars and a street map of London.
Continuity mistake: His Bankship visits Poirot during the evening, and begins telling him the story of the silver mine. "For half a century, men have died", he says. Poirot has the magnifying lens in the right hand, but also the rock in the left; cut to a different angle, the hand with the rock is held low, out of frame, and then back to the first shot, with the rock exactly where it was. (00:11:55)
Continuity mistake: The cream colored shoes of the Lady are prominently featured in the finale. When the actress has to run, not only are the heels replaced by modern tennis shoes, but they're black, in contrast with her white stockings. (00:46:40)
Factual error: To meet The Veiled Lady the second time, Hastings and Poirot go to the Natural History Museum. The establishing shot is the iconic "Dippy the Diplodocus", right in the main hall. But in 1935, Dippy would have been in the reptile hall instead, and with his head and neck mounted differently. (00:37:35)
Continuity mistake: Poirot tells Miss Lemon to calm down because "It is only the simple blackmailer." Pauline Moran has her right hand on the bag, but in the close-up that follows her hand is at a distance from it. The difference in position (and thus in the takes being edited together) is reflected by a mistake happening a few seconds later, when you can notice as she turns around to answer the door, that her gloves have also switched hand. (00:12:10)
Continuity mistake: When Poirot and Hastings enter the Athena, there's an establishing shot as they walk to the right of the concierge. In the following shot, some elements like the lady with the flower dress by them are consistent, but the desk employee is suddenly on the phone and a bellboy appears by the stairs. Also the lady in the corner changes from a blonde to an elderly woman in a red coat. (00:05:50)
Other mistake: Poirot, Hastings and The Veiled Lady go upstairs because the lobby is 'too public'. The man spying on them is hiding behind the same newspaper prop used in the previous episode of the season, where Hastings was reading it in Cornwall at the beginning. So must be a pretty old issue now (Peril at End House takes a few days, and they were on holiday). (00:07:40)
Continuity mistake: Sitting on the park bench, Japp narrates the jewelry heist to Poirot. The passersby during the scene change in the various angles, and the most evident demonstration is offered by the fella that starts his walk exactly when Japp sits down. Grey pants, a sleeveless vest and hat, he walks all the way to the path in the background and exits stage right. But he's walking behind Japp when he says "The stones in his pocket were not the real stones." (00:03:00 - 00:03:45)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: In the first scene with the 'G-Man', the room in the shots with the camera roughly by his shoulder is lit in a different way, with his body fully in the 'sun'. Especially visible when he picks up the phone and starts spouting yankee-isms going all "Yeah yeah so what yeah." (00:09:00)
The Disappearance of Mr. Davenheim - S2-E5
Continuity mistake: The race is presented through actual footage of the era, with a cameraman from Pathe shown, saying that Lowen's car is number 3. But the car shown in the stock footage is different from the one Lowen is driving, which does not even have the number in the same position. (00:33:10 - 00:33:45)
The Kidnapped Prime Minister - S2-E8
Continuity mistake: At Scotland Yard, Poirot is readying the glasses for the moment when Japp will pass him the paper he's reading, about the driver. When the view switches, his hands, that were above the desk level, start off from underneath the desk. (00:33:35)
Character mistake: The rude doctor says that Edward Pengelley "wouldn't poison his grandmother's dog", to which Poirot irately blurts out "but it is not the dog of Madame Pengelley's grandmother that has been poisoned." He should have said "of Monsieur Pengelley." (00:12:50)
Continuity mistake: At the beginning of the opening credits, there is a close-up of the model boat pushed forward. It passes by a kid who is hunched over, hands on his thighs. Wider shot, and the kid just watches the sailboat pass by standing apathetically. (00:02:15)
Continuity mistake: When Japp does the comical fistwave at Poirot at the end, Poirot's carriage is passing by a line of people (woman with red coat, young woman with greenish one) that already passed by when the constable was giving the 'bad news' to Japp. (00:48:20)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Miss Lemon, as Penelope Maitland, enters the performer's room. The shady character that opens the door does it holding a cigarette in his left hand. The hand is kept close to his chest in one shot, while it's on the door in the reverse. (00:31:35)
The Adventure of the Western Star - S2-E9
Continuity mistake: In his preparations for the arrival of his idol, Poirot sets a flowers bunch with a card ("Mlle. Marie Marvelle"). When we see the bunch later as Poirot has to leave to go to her, the card is absent - but he has not touched the table. (00:03:55 - 00:05:15)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Poirot is doing his round of phone calls at night clubs looking for the chanteuse; the pen before Hastings' arrival is pointed to the left side of the screen, when he sits down (and Poirot has not touched it) it points to the right. (00:24:40)
The Adventure of the Western Star - S2-E9
Continuity mistake: Japp shows his documents to the two policemen who caught him lurking in the bushes; when he says "Twigez-vous?" he's holding the card by the corner, while in the reverse shot ("Oh, very sorry, Sir") he's holding it in the middle. (00:25:30)