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)
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: 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)
Four and Twenty Blackbirds - S1-E4
Plot hole: In the denouement, Poirot says explicitly that the culprit sent the letter to the victim - but the letter in question, in this dramatization was stated earlier (in a change from Agatha Christie's original) to be an invitation to the art gallery, and the culprit is not the manager/art gallery owner! In the actual short story the letter was a personal message of entirely different nature, written and authored by the culprit.
Four and Twenty Blackbirds - S1-E4
Continuity mistake: When the milkman places the third bottle on Mr. Gascoigne's steps, they are placed in the sun. When the neighbour approaches, the whole road shows no particular sunlight. Which is fine, as a sudden change of that kind is ordinary. When the other neighbour pops by the corner and inquires, there's a close-up of the bottles, and again there's visible and directional light, pointed differently than the first instance. (00:08:45)
The Adventure of Johnnie Waverly - S1-E3
Plot hole: Forgiving the implausibility that nobody checks their own watch at the time of the kidnapping, the clock in the living room strikes 12 supposedly ten minutes early: everyone blindly storms from the room when the chimes have not yet ended, and reaches the supposed perpetrator who is by the side entrance. They talk to him briefly and the clocktower signals now the real noon. It's hard to see how 10 full minutes could have passed, and even harder when everybody runs back to the house, to find the clock there signaling 12:11: it took them a mere minute to get there, what took them so long the first time? (00:30:00 - 00:31:30)
The Adventure of Johnnie Waverly - S1-E3
Plot hole: When he is taken away from the mansion, Johnnie is hammering with his fists on the car windows, as if he was genuinely in distress and resisting the kidnapping. But as we know, that's not what is happening, he knows his captor well and came willingly. (00:31:25)
The Adventure of Johnnie Waverly - S1-E3
Plot hole: In the original story, it is made clear that Mrs. Waverly is the one in the family with the wealth, but it does not go as far as having everyone, guests included, eat plain rice and boiled potatoes, and have the mansion dilapidated with restoration work left unfinished for years. This creates several plot holes: nobody would be interested in asking lavish amounts of ransom money to people who live an impoverished life, and most importantly, the husband would never be able to justify being able to have enough money to suddenly resume construction work on the house (in the original, he simply wanted to use it as spending money).
The Adventure of Johnnie Waverly - S1-E3
Character mistake: Contrary to the short story, here Mr. Waverly consults Poirot not accompanied by his wife, and by his own initiative without even telling her at first. Given the solution of the case, this appears to be completely illogical.
The Adventure of Johnnie Waverly - S1-E3
Character mistake: When the ever gallant Poirot meets Mrs. Waverly, David Suchet hesitates for a second awkwardly as he mistakenly went for a handshake when Julia Chambers offered him a limp downturned hand instead. Not quite the kind of social faux pas Poirot would be caught into. (00:11:55)
Factual error: This episode happens on the first days of November 1935. During the 5th of November fireworks Hastings, Japp and Poirot walk at night through streets with plants prospering and in full green, and the same happens during the visit to the golf course.
Factual error: As Japp and his moustached pal visit the nightclub in search of Major Eustace, the song "Hindustan" is executed. While it is a song perfectly believable for the year (stated as being 1935) since it was written in 1918 and a huge hit, the version played here is quite a bit different, sounding a lot more like the upbeat version heard first in the Rosemary Clooney-Bing Crosby album "Fancy Meeting You Here", which had other classics reworked for the duet formula with added lyrics - exactly like in the back-and-forth heard here between the singer and the band. Said album came out in 1958, though. (00:30:20)
Continuity mistake: During the conversation with Laverton-West at the pool, in the close-ups of Poirot and Japp there are always two gentlemen chatting poolside near the bench where the politician dropped the towel. In wider shots, that's not always the case - plus, one of them walks away without a towel but he's back wearing it. (00:27:50 - 00:28:50)