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)
Continuity mistake: Miss Lemon's ice cream quite literally melts between shots (and the actress ignores the dripping on her fingers). (00:51:15)
Continuity mistake: When Poirot shows Freddie the bullet, in the close-up his hand is right by the sugar bowl, but he was shown putting the cigarette holder at greater distance, closer to Freddie herself. (00:25:05)
Audio problem: Nick gets supposedly grazed by a bullet fired while the plane's noise has already diminished considerably, making quite unlikely that any gunshot could be drowned out by it. (00:06:50)
Continuity mistake: Poirot shows Hastings Nicki's hat; he holds it in a different way (using the thumb to pinch, or with the light brim tucked in between index and middle) between shots. (00:08:55)
Continuity mistake: Poirot and Hastings are eating after their first visit to End House. During the entire scene, natural light changes in intensity depending on the angle of filming. (00:20:15 - 00:21:10)
Continuity mistake: During the sentence when Hastings tells Poirot he's got "No imagination at all", the lady sitting behind the Belgian faces the other way between shots. (00:02:25)
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: 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)
Factual error: Jim Lazarus drives a Vauxhall DX (14/6 Light Six) Stratford Tourer, a 1936 model. This episode takes place in the summer of 1935. (00:46:20)
Continuity mistake: When Poirot stands as his employer sends him packing, the shadow projected on the back wall is taller than the cupboard by a good margin, roughly from the shoulders up. In the close-up that follows, Poirot is standing in the same spot when he replies "I shall not fail to do so", but the shadow is shortened considerably. (00:14:50)
Continuity mistake: As Poirot, holding the family picture, turns around to ask Mrs. Oglander about the kids in the portrait, he suddenly has his finger near the middle of the frame, much higher than before. It keeps going up and down during the conversation. (00:36:40)
Continuity mistake: Ralph Walton flubs the line and breaks character walking off set: he begins undoing his collar. He repeats the same action ('begins' to undo it) next time the camera is on him, and during a cut when he is in frame both shots, his hands jump off/on the collar. (00:04:35)
Plot hole: Hastings came over to assist Poirot in his case, posting guard overnight. He offers to drive Poirot back to the villa since Poirot is in a rush and has figured out of the culprit. Poirot approaches the villa just in time to come across Mrs. Vanderlyn on her way out. Poirot rushes to Hastings then to give chase to the woman but...Hastings has pulled out all the plugs and is cleaning the carburettor, just doing some random maintenance to the car that would take him, in his words "an hour" to bring back to work. On a one-day job, Hastings crippled their own car for no reason whatsoever. This is beyond stupidity.
Continuity mistake: When Mr. Russell interrupts Hastings' plans of randomly shooting in the middle of the Alexandria harbor, an empty brandy glass is on the table next to him in the first shot, and comes closer the second time he's in frame. (the two shots are not strictly consecutive but there's no reason why the frail old man, still in the same position both times, would pull his empty glass a couple inches closer when off-camera). (00:26:20)
Continuity mistake: Clapperton demonstrates how he can deal cards of his choosing at will and therefore he refrains from playing bridge. In the close-up of his hand and table you can see the cards he dealt are stacked irregularly, but when he deals the last 4s the cards are more neatly arranged, spread in a fan. (00:17:10)
Continuity mistake: Sitting down with Miss Lyall as she coughs, Valentine invariably has her left hand up when shot by the right side, just the elbow on the armrest, while every time she is shot from the left side she has the whole arm leaning on the chair, hand down. (00:29:00)
Continuity mistake: Poirot at the ruins meets Mrs. Gold, and he starts telling her more about the local findings. You can see in the faraway shot how next to the fence two guys are working by the goat. One of them has a black beret, the other the typical saharienne outfit. Change shot, and as Poirot lets out a "What a beautiful day" remark, the dude in black becomes another man in khaki instead. (00:13:20)
Continuity mistake: When Jimmy reads the solicitor's letter, the date is 5 October 1935. Hastings wrecks his car here but in Murder in the Mews, taking place on the 6th of November, he has it again. Assuming that he has been able to get his car back to form entirely restoring/replacing the ruined sections (Japp tells him that it's now just "an expensive scrap of metal"), in that episode the car needed ordinary maintenance work, while going by the events of this episode it would have been fresh off the car shop instead.
Character mistake: As Poirot reconstructs the facts in the flat (and he explicitly says "consider the FACTS"), he lays out that "a letter which was found at the scene of the crime with John Frazer written on the bottom." But the letter simply said "Frazer", the first name was just Japp's random conjecture based on the initials on another evidence being J.F. (00:27:40)