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).
Continuity mistake: The Countess arrives at the hotel at the beginning of the episode. In the overhead shot she reaches the top of the stairs with nobody close to her, just the porters behind her, but in the next shot there are other people in the lobby, who at the next cut are even closer to her to fit in frame. (00:02:10)
Continuity mistake: During the exhibition of the much acclaimed contralto, at one point it is shown that Lady Runcorn is going upstairs and is looking at the smoking person. Back to the host who is on his own at his table. At the first cut, suddenly there are more people standing in attendance in the background (pretty much everyone was seated earlier) and his glass has also refilled. (00:10:15)
Factual error: Attention to detail in props is always extremely high in this series, and tubular flashlights have been in circulation since the beginning of the century. However the one that the supposed burglar is holding as they make their way through the top floor of the villa looks perfectly modern and unlike any model compatible with the 30s. (00:10:20)
Factual error: Hastings and Miss Lemon decide to investigate on their own. In the outside view of the first suspect they go question, a large contrail is visible on the left of his building (contrails were not a complete impossibility in the 30s, but it's rather odd to randomly see one in an establishing shot for this timeframe). (00:22:40)
Factual error: Poirot is visiting an art exhibition with the Countess, and expresses his admiration for a painting by Marc Chagall. Amazingly enough, that painting is "Les Plumes en Fleurs", something Chagall will create in 1943, years after the time when this pre-WW2 episode takes place. (00:24:50)
Continuity mistake: At the end of the 'lovely day' with the Countess, Poirot stops a cab and opens the door for her. Just before the cut, notice a woman with a white dress and a brown hat crossing the street in front of the taxi. The extra crosses the street again in the same direction when he says "Oui" in the following shot. (00:28:50)
Character mistake: Hastings and Miss Lemon return to the apartment after their visit to the various suspects. Hastings though closes the door leaving the key in the hole, outside. (00:29:20)
Plot hole: Since the Countess was the only person to be at every dinner when the jewelry thief was in action, it takes a very special kind of idiot to not identify her as the culprit. Japp here did not need at all Poirot's acumen, but simple due diligence cross-checking the guest lists, something there is absolutely no reason he wouldn't do, and yet she is never treated as a special suspect. Also, Japp's job is described as being in jeopardy after the first 3 thefts, a 4th happens, he does not quite solve it (but retrieves at least the necklace), but he's off the hook despite the thief being unidentified, at large and with still the jewelry stolen from the first 3.
Factual error: At the party, Marcus Hardman tells Bernard that the Countess recently arrived from Russia, and she describes herself as being in exile. Which made sense in the source material, set right after the Russian Revolution, but less sense in this adaptation, set in the mid 1930s. If she stayed in Russia that long, she would have spent 15-20 years with zero privileges from her rank at that point, and nothing from her old wealth, seized by the communist government.
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: When Major Rich is interrupted playing billiards, the shadows on the playing table have inconsistent angles between shots. (00:11:30)
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: During the party, the colonel expresses to Poirot his disappointment for the jazz record being played, music "from the inferior races." He puts a tart in his mouth, closing his lips past the piece of fruit. Cut to the wider shot, and he is still holding a tart that sports the strawberry he just chewed on. (00:19:00)
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: Poirot enters Japp's office when the inspector is dealing with the tribulations of modern machinery. As Poirot sits down, you can notice the crumpled paper by the phone being different in the reverse shot, when you can also see Japp's hand being at the corner of the typewriter. But he brings it up from his lap in the next shot. (00:38:15)
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: When Poirot pulls out of the drill hidden in the handle, he holds it triumphantly in his right hand. In the next shot he mounts it on the handle starting the motion with the drill already in the left hand and the rest of the gimlet in the right. (00:40:00)
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: Japp hands Poirot the phone in his office holding it with the left hand, which turns into the right hand at the cut. (00:40:10)
The Mystery of the Spanish Chest - S3-E8
Continuity mistake: In the flashback during Poirot's narration, the scene with Colonel Curtisstalking to the victim at the military club happens differently from the first time around, with Clayton switching hand position after a different line of dialogue, starting off in discontinuity with the previous shot (originally the continuity was flawless). (00:44:40)