Continuity mistake: Poirot meets Hastings about to go play golf with a Stiffie. Hastings holds his hat by the brim, which turns into the crown in the reverse shot. (01:02:05)
Character mistake: In the hotel lobby, Poirot, indignant of Hastings' attitude towards the murder case, says "After three attempts had been made at the life of M. Nick, Poirot gave his word he would protect her." But he did that after four attempts; Nick already avoided 3 "mysterious accidents" (painting, car, boulder) and Poirot witnessed the 4th, the bullet that pulled him into the whole case to begin with. (01:02:20)
Continuity mistake: Commander Challenger in front of his boat laughs with Hastings "I hope my alibi is in order." As he says that, Hastings nods. During this close-up, his hat is casting a completely different shadow, covering his whole shoulder instead of just the back of the neck as in the rest of the scene. (01:03:35)
Continuity mistake: When Japp talks to Poirot and Hastings about the gallery troubles, the peppermint rock candy he is waving is wrapped differently between shots. (01:13:40)
Continuity mistake: Starting the seance, Poirot ask everyone to hold their hands. Lazarus barely stifles a laughter. Between that shot and the previous, his hand goes from above the table to underneath it. (01:38:25)
Plot hole: The hole in the hat was pre-existing and the bullet was fired in advance and dropped. Poirot notices immediately the hole when Nick puts the hat down but somehow missed it while she was wearing it as she supported him. He also does not notice that the bullet has not been fired at that time - which would have been still hot if just fired, not at all if dropped. Most importantly, in the spot where they were sitting, it's not even possible to think where a shooter could have ever been hidden; nobody wonders where the mysterious shooter could have been or cares to investigate the circumstance despite knowing the very moment the supposed shot happened. The fact is basically ignored throughout the rest of the episode.
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.
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: 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)
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: 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: Lavington puts his hat on the couch before talking to Poirot. The hat shifts closer to Hastings and then back closer to the armrest during the scene. (00:12:45 - 00:14:30)
Continuity mistake: Lavington arrogantly sits in Poirot's study and opens his cigarette case, closing it after. In the following close-up, the case is open again. (00:13:15)
Revealing mistake: The phone book has a LMS logo on the page edges in the close-up where we see Poirot actually flip through - the logo disappears when he is moving the book in the rest of the scene. (00:16:10)
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)
Revealing mistake: The stuntman smashing through the window is quite obvious - he does not even have the hair styled like Hastings'. (00:31:30)
Continuity mistake: When not-so-Lavington is spying Japp and Mad Dog Poirot outside of the station, he is holding the wheel with his right hand at the top, but a moment after he's using that hand to smoke instead. (00:34:35)
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: When the box opens revealing the jewelry, the jewelry is scattered differently each time it is seen. The box itself gets closer to the table's edge when the lady nabs the jewelry. (00:40:40 - 00:42:40)
