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.
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)
