The Mysterious Affair at Styles - S3-E1
Plot hole: To enter Mrs. Inglethorp's bedroom, Hastings and John have to ram the door and certainly break the lock (it is replaced, so there was damage done). The doctor leaves the house very early in the morning just after ascertaining the death of the woman, and tells them he "locked both rooms" (the room has three doors but one is bolted internally, allegedly). But the door was broken, and in fact when Poirot arrives, which is early in the morning, as Hastings went to the village waking him up, he finds a brand new lock in the door. They would have needed to summon a locksmith at maybe 6 or 7 am, to repair an internal door in a country house, and he should have done it on the spot (also, the door frame itself is more likely to suffer damage than the lock itself, no real damage was shown during the scene). The keys are also all in the same bunch and not looking in any way different (one should be brand new and shiny). (00:28:45 - 00:37:40)
The Mysterious Affair at Styles - S3-E1
Plot hole: Can't fault this massive plot hole to the adaptation, but to the source material; the culprit (forgetting the stupidity of writing an incriminating letter detailing the plan to murder someone, and put it in a desk he shares with her) since there are people outside the room that are about to enter, tears the letter in 3 neat vertical strips, rolls them, puts them in the vase on the mantlepiece, and then opens the side door to slip away...instead of simply pocketing the letter and going through that same door. Nobody was going to search him or anything and could have burned it, torn it into confetti, anything, later. It takes way way longer to do what he did, which needed him to stay there in the room increasing the chances of being found out. And of course he and his accomplice do not retrieve the letter after.
Wasps' Nest - S3-E5
Plot hole: There are some additions to the original short story in this dramatization, but they create a little problem since Hastings does not come with Poirot for the finale, and in fact is told to stay home in a rather demeaning way. Without Hastings, it's hard to imagine Poirot could break into Langdon's house, since Capaldi when is not playing creepy clown is a sculptor working at home; Poirot would need an accomplice to create a diversion. And, even sillier, Poirot tells Hastings to go buy him some washing soda, but he needs the soda to pull off the switch. Hastings should have joined him at least to give him the soda once Poirot has visited the doctor.
The Tragedy at Marsdon Manor - S3-E6
Plot hole: The murderer is in possession of chloroform from the doctor's cabinet, but there's no realistic timeframe when they could have done it, nor any explanation why the doctor notices it completely at random when Poirot visits, just approaching the medicine cabinet, something he routinely opens and looks through during the day.
The Tragedy at Marsdon Manor - S3-E6
Plot hole: The murderer planned everything making it seems accidental. They perfectly managed to fool the coroner and need only to be alone at the mansion to get rid of the murder weapon. So what they do is...they go through great risks to make everyone know someone tried to murder the wife too, making it obvious that there is a killer at large, which only makes the investigation more stringent and most importantly, keeps the police on the premises for surveillance preventing them from disposing of the weapon (like almost everything in this episode's plot it is not a flaw of the original story, but of the dramatization, who added practically every minor character).
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).
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.
