Continuity mistake: When Gertie and Joey make their escape running down the stairs of the hall, they pass by a couple (she has a white hat and a blue dress). When Poirot and Japp run after them, the same couple has jumped back several meters. (00:43:00)
Double Sin - S2-E6
Continuity mistake: In the car chase, when the woman turns to check the police behind them, the close-up on the steering wheel does not match the position of her hands before and after. Similarly her passenger has the right hand visible when it shouldn't be. (00:28:45)
The Disappearance of Mr. Davenheim - S2-E5
Continuity mistake: When Poirot does the newspaper trick for Miss Lemon, the final reveal has him present the newspaper holding it between index and thumb in the front view, index and middle with the thumb sticking out in the back view. (00:42:10)
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)
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)
The Disappearance of Mr. Davenheim - S2-E5
Other mistake: When Japp and the bobby arrest the pickpocketer, the dialogue says "It was only last week that we put him inside for three months" which obviously does not make sense. In the original story he did the 3 months of jail the year before, and this has to be a flub in the lines of this TV version (it is specified also that he did those in the winter, so the Sergeant can't possibly mean that he was released last week). (00:35:00)
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)
The Disappearance of Mr. Davenheim - S2-E5
Continuity mistake: Carving the distant relative of his parrot for dinner, Poirot slices one side in the close-up, which turns out to be the exact opposite side in the wider shot. (00:38:35)
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 Disappearance of Mr. Davenheim - S2-E5
Continuity mistake: When Poirot at dinner asks the first question (the bathroom one), he does not have his large napkin in his vest. When he asks the second one (the bedroom one), the napkin he had for all the rest of the scene is back. (00:40:15)
The Kidnapped Prime Minister - S2-E8
Factual error: When the former Mrs. Daniels hops on her car followed by Hastings, between them you can see a speed bump, not a feature on roads in Britain (or anywhere) at the time. (00:36:55)
Factual error: Poirot is cycling through Wimbledon; he passes by a house which has a definitely non-1930 car in the yard, and a yellow alarm box on the first floor. (00:18:20)
Continuity mistake: Poirot rudely awakens Hastings with his three questions. You get a good view of Hastings' wristwatch on the bedstand. When at the end of the Q&A Hastings turns his attention to the watch, it is in a completely different position. (00:41:25 - 00:42:35)
Revealing mistake: The stuntman smashing through the window is quite obvious - he does not even have the hair styled like Hastings'. (00:31:30)