Other mistake: The closing credits on the DVD are for another episode, "The Kidnapped Prime Minister." (00:47:15)
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 Adventure of the Western Star - S2-E9
Continuity mistake: When Lord Yardly is offering wine to Poirot, in the aerial shot Hastings has both hands over the glass, but his hands are in a different position in the consecutive view. (00:20:20)
Plot hole: The whole premise of the plot is that nobody is staying at End House but Nick (and the servants); she even says explicitly that there is just one room that is usable and everyone else stays at the Majestic. During the party though, Freddie tells Maggie to go get her coat which is "in my room." They are at End House, not the hotel, how would Maggie have a room there? (00:35:00)
Plot hole: The killer's plan needs to have Maggie at End House - but it's achieved through Poirot's proposal to have Nick call her to act as added protection. But this makes no sense; Maggie's presence would have not protected Nick in any of the alleged attempts to her life; the frame would have crushed her too, she would have died in the car, she couldn't have prevented the rock from falling, and Nick was shot while the most famous detective was with her, even! A random little girl from Yorkshire would have not mattered, so it makes no sense that Poirot endangered someone for no gain.
Factual error: Poirot has just suffered "a turned ankle", in his words; he's talking with Hastings and the kind woman who helped him out, when their conversation gets perturbed by the noise of a plane. Which is surprising, since the plane in question is a Volmer VJ .22 Sportsman, a plane from the 50s, way after the 1930s setting of the episodes. (00:06:40)
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)
Audio problem: In the very first turn of Monopoly shown, the player scores 11, but moves just 7 ticks. In the second, a 9 produces 8 ticks. (00:01:40)
Suggested correction: It is entirely plausible that a player does not tap the piece to the board with every move. Sometimes, you tap it hard enough to make a sound; sometimes, you just hover the piece over the square.