Plot hole: Nobody hears the sound of a gun being fired past a door they were waiting almost in front of, and the police cannot tell apart a shot fired point blank by one fired 20 feet away and probably at a very sharp angle. Moreover, the bleeding should be all over his face, since leaning the way it is shown in this adaptation is most likely to lead the victim to fall over, and even leave bloodstains out of the window and on the ground below, which someone would have noticed in the crowded factory.
Continuity mistake: Poirot is holding up a letter in an envelope. He turns it to show the front to Lady Mayfield. The flap of the envelope appears to be tucked in. The shot cuts to a close-up, but now the back of the envelope is facing Lady Mayfield and the flap is sealed. He then turns the envelope to show her the front. (00:44:20)
Factual error: Throughout the episode there are sections of dialogue in Greek, which are deliberately left untranslated. The subtitles frequently transcribe the Greek inaccurately. For example, the Greek girl who assists Poirot and Lyall in finding out about the poison says "Elate!" to them, which means "Come!" said to more than one person, but this is transcribed in the subtitles as "Ella!", the form used to a single person. Later on, the girl's grandmother says "Ohi enas Anglos anthras. Mia Anglitha yineka. San esena" ("Not an Englishman. An Englishwoman. Like you"), but this is given in the subtitles as "Ohi enas Anglos anthras, che yenika. Son ethena", which doesn't make sense. (00:40:45)
Other mistake: Mrs Vanderlyn holds a letter out of the car window and calls to the chauffeur to take it. She calls him "Dixon" but the subtitles read "Gibson". (00:37:05)
Factual error: Poirot and Lyall speak to people in the street of Rhodes, looking for someone who can tell them about the poison. The people they speak to all shake their heads, but Greeks do not do this to say "no" - they tip their heads back. (00:39:40)
Factual error: At the end of the report on the findings of the crime scene, the "Italian" inspector tells to his subordinates what literally would translate as "Removes this meddler from here, no more access to the prisoner, that you understand?", which is just wrong in accent, cadence and construct. (00:36:30)
Deliberate mistake: The day of his scheduled departure, Poirot overhears conversations (mainly the one from the window of his room) he couldn't possibly be hearing given the long distance outdoors and the tone of voice. His reactions are shown as if he could hear and not simply see and infer the meaning. (00:23:00)
Revealing mistake: Poirot is sitting reading the paper with the front page visible to the viewer. A breeze ruffles the pages and reveals that the interior pages are blank. (00:14:10)
Factual error: The machine guns on the plane appear to be cannons, which were not introduced until much later.
Factual error: The basis of the blackmail is based on the Japanese invasion of Manchuria because howitzers were supplied to bombard Shanghai. Shanghai is not in Manchuria. (00:35:41)
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)
