The Disappearance of Mr. Davenheim - S2-E5
Plot hole: The killer has a perfect (in movie logic at least) plan but he amplifies its risks to 1000000% getting caught on purpose with an incriminating item that links him to his secret identity and that is amazingly likely to have him questioned and face the wife of the deceased (who recognizes him in 0.5 seconds) and other witnesses. Even without Poirot it is impossible to imagine a trial happening without him having to appear in some capacity. And in this TV dramatization, the motive of Lowen to hate Davenheim is obvious, but not the other way around, so it appears even more baffling that he'd utterly ruin his perfect escape just to mess with a rival apparently he had a upper hand on. Moreover, the dramatization makes his plan even more absurd, as instead of pawning the valuable ring like in the original and being only marginally involved, here he has it days after the murder, and robs the Inspector chief! Any bobby would do. Finally, here he also wears prosthetics, again drawing attention.
The Disappearance of Mr. Davenheim - S2-E5
Plot hole: The safe is behind a painting that acts like a real door. When Mrs Davenheim spots it, it's wide open. But Japp questioned her in the same room and the painting was in place back then. It really makes no sense that with a story depicted as being so big (it makes the first page of the national newspapers) and with an investigation in place, nobody in a week has checked the safe at all. (00:27:50)
