Continuity mistake: As the two porters are carrying the piece of furniture, the draping on top of it goes all the way down one side when they have just unloaded it from the van, and the opposite side when they are bringing it up Whitehaven Mansions' stairs getting cranky at the doorman. (00:01:40)
Other mistake: When Hastings pulls Poirot's slip of paper out of his pocket, he's reading it upside down - as you can see from the close-up, the torn up part should be at the bottom, not at the top. (00:11:40)
Continuity mistake: Once Poirot hypothesises that the lightbulb could have been replaced, he curls back his finger pointed at the young fellas. New shot, and he is back pointing fingers. (00:18:45)
Continuity mistake: As Poirot stands from the late dinner with the young socialites to go talk to Inspector Japp next to the door, he leaves his napkin on the table. The napkin changes between shots, going from mostly straight to crumpled (when Mildred says "How dreadful!") to straight again. (00:22:20)
Continuity mistake: During the entirety of the scene in the kitchen, Patricia keeps her hands in her lap, but they change repeatedly from being side to side, to her right hand lying on top of the upturned left. (00:22:40)
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)
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: Somehow, Poirot is the first person to get to the basement - he obviously would have slowed down terribly the policeman and the young and spry Jimmy rushing down the stairs with him.
Other mistake: At the very end of the episode, Miss Lemon stops talking as if she could see Poirot glaring at her above the newspaper - while in fact, he is facing the other way.
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)
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)
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)
Continuity mistake: When Pamela Lyall is talking to Poirot before his scheduled leave going as far as wishing there were a murder so he could stay, her right hand moves on and off the table between shots. (00:24:20)
Other mistake: The man in front of Poirot in the line to embark argues supposedly in Italian with the officer: he does it in broken Italian but trying to pronounce informal words (even an incredibly explicit and vulgar curse at the end!) with unnatural cadence and a very thick Spanish accent. (00:28:30)
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)
Factual error: When Poirot leaves customs with Mademoiselle Lyall, one of the supposed Italians asks in that language "What's happening, what is this noise?", which does not make sense in context, especially with the officer just shrugging and showing him the card. (00:32:55)
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)
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: 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)
Visible crew/equipment: At the very end of the episode, as Poirot's car drives off headed to the harbor, filming equipment is neatly reflected in the door. (00:51:40)