The Disappearance of Mr. Davenheim - S2-E5
Continuity mistake: During the conversation between Lowen, Hastings and Japp through the car window, in his close-ups Tony Mathews moves his torso closer to the window and then back towards the wheel, several times. That is not always reflected accurately in the reverse shot with just the shoulder visible. For instance, right at the end of the scene, he leans in saying "Good God, you don't think you can keep a thing like that secret, surely", but his body is exactly in the same spot in the shots before and after. (00:24:20 - 00:25:10)
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: Japp taunts Poirot, presenting him with the mystery. While he does that, he turns around towards himself the magic book. When he leaves, Suchet reaches for the book that is more distant from him and turned the 'right' way. (00:12:00)
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 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 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: When Poirot's castle collapses, the cards are all in perfect order, but become scattered after the cut to Japp. (00:35:40)