The Million Dollar Bond Robbery - S3-E3
Continuity mistake: When Poirot says "I'm sorry" to the culprit, he has the hand on the shoulder of his accomplice. Her hair is on and off that shoulder in a blink. (00:48:35)
The Million Dollar Bond Robbery - S3-E3
Continuity mistake: After Ridgeway puts down his Queens High, his hand is hovering slightly on the table, but at the cut it is arched, fingers pointing on the table. (00:28:55)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Cynthia is sobbing with Hastings, and he asks her to marry him. The handkerchief in her hand changes position between shots (particularly easy to spot when you look at the black band). (01:13:05)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: After Hastings reminds him of the mantelpiece, Poirot shouts "Mon Dieu!" and pounds the table. The cards scattered on the table differ in disposition between shots when he stands. (01:21:05)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: When Hastings spots Poirot from the window as he arrives for the denouement, his hand is in a different position on the window frame (left or right of the vertical bar). (01:26:55)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: At the hearings, the doctor is on the stand and says "There was no strychnine in it." Mr. Wells closes his fountain pen. But then in the next shot he holds it in his hand. (00:52:40)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Poirot locks the document case in a close-up. The shadow on the case is at the center of the object, but in the wider shot it is projected entirely on the left side. (00:38:15)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Mrs. Inglethorp's death happens with her having a much messier hair and the neck tilted to an angle in the wider shot, compared to the close-up on Gillian Barge. (00:30:00)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: When Hastings tries the fake beard on, it sticks past his fingertips more in the shots from behind than on the front. (01:09:15)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: The larger broken porcelain pieces Poirot is examining in front of the fireplace change place between shots. (00:39:45)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Hastings has just met the Ingelthorps, and now is outside so John Cavendish can introduce his wife. In the wide shot it's evident that John lowers his arm, but in the closer view his arm is still held up high before Mary speaks. (00:08:10)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: The first time Mrs. Ingelthorp is shown, she is holding a pen. In the second shot she is holding it in her right hand, while in the third she has the lid of the pen in the right hand and the pen itself in the left. (00:07:30)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Hastings receives the messages that he is wanted by someone outside the movie room; you can see the person sitting next to him turn towards him in the first shot, and re-turn towards him in the following. (00:02:25)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Everyone is silent at dinner after Miss Howard left, but Mr. Inglethorp keeps a healthy appetite. As he eats, look at his plate; the shadows cast on it switch side depending on the camera angle. (00:18:40)
The Mysterious Affair at Styles - S3-E1
Continuity mistake: Mary Cavendish's wine glass goes from almost empty to full and vice versa several times during the dinner scene the first day. (00:10:10 - 00:11:10)
The Tragedy at Marsdon Manor - S3-E6
Plot hole: It is revealed towards the end of the episode that the painting Mrs. Maltravers did when the murder took place was not painted that day and that time of the day, because it had the wrong shadows. But we actually saw what was on the canvas when the secretary was leaving to go to the bank, and it was that exact painting in an early state. She also came up with the idea for the murder the night before, making even more unbelievable that she'd just have the alibi painting ready and waiting the morning after. That without mentioning the fact that the murder itself as described is not something that would have required an amount of time needed to make a whole painting, and that she could have finished it later anyway (she gave it to Hastings a day later, after all).