The Adventure of the Clapham Cook - S1-E1
Continuity mistake: Hastings is reading a letter that makes him go "Good Heavens." He is holding the letter by the top left corner, which becomes the top right in the (lack of) reaction shot from his Belgian friend. (00:24:20)
The Adventure of the Clapham Cook - S1-E1
Continuity mistake: When the mysterious Aussie lawyer gives Miss Dunn his card, he hands it to her with the fingertips pinching the paper in the top corner, while in the reverse shot he's holding it by the bottom corner. Also, just a moment later she gives it back to him using her right hand. Unfortunately, the card was in her left hand. (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)
The Adventure of Johnnie Waverly - S1-E3
Continuity mistake: When Hastings stops his car in front of the train station at the end of the episode, he talks to Poirot holding his hand on the outer circle of the steering wheel, or on the inner part in the reaction shots. (00:49:20)
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)
Four and Twenty Blackbirds - S1-E4
Continuity mistake: Hastings carries the picture of the two brothers from Dulce to Poirot holding it by the bottom, top, side, depending on the angle. (00:13:45)
Four and Twenty Blackbirds - S1-E4
Continuity mistake: As Poirot and Hastings watch the farce, the sword gets grabbed from the table by two hands, the left one doing the lifting by the handle. But the comedian in the following shot has it in his right hand. (00:32:04)
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)
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)
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.
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 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)
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: As the future victim scoffs saying "Must be a great solace to you" to the Tollivers, his hand goes from midair to the teacup between shots. (00:11:30)
Continuity mistake: Mrs Clapperton puts down the score notes and pencil before lighting up her cigarette. Between the shots and the reverse, the pen disappears and the notebook changes position. (00:13:35)
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: 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: When Miss Henderson gets back aboard, the same extra (bearded man with black robes and brown belt) walks by coming from both directions at once. (00:26:30)