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.
Continuity mistake: Poirot is holding up a letter in an envelope. He turns it to show the front to Lady Mayfield. The flap of the envelope appears to be tucked in. The shot cuts to a close-up, but now the back of the envelope is facing Lady Mayfield and the flap is sealed. He then turns the envelope to show her the front. (00:44:20)
Trivia: Poirot in the ship's lounge is reading the actual May 1st 1935 issue of Bystander (recognizable by the cover and with the correct page order, does not seem to be a simple movie prop), roughly consistent with the time frame of the first season and a contest taking place on the 14th. (00:07:50)
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