At 1:18:32 and minutes prior, during conversation with Eloise Renauld and Stonor, Poirot wears a tan/beige paisley bow tie. At 1:18:38, when he stands, Poirot wears a red paisley bow tie. Upon leaving the house at 1:19:06, the tan/beige bow tie returns.
At 41:47 Hastings pays the bill for the tea with Bella Duveen. He puts some bills on the table but he drops a bill. He looks at it for a second but continues like nothing happened.
In the coroner's office there's a calendar on the wall, clearly revealing the date in French - 18 Mai 1936, Mercredi (Wednesday). In 1936, however, the 18th of May happened to be a Monday.
At 1:04:22, Hastings lifts up a photograph of Bella. It is a front-facing bust shot portrait of her with arms at her sides. Within the next 10 seconds, Poirot has taken hold of it, and a closeup is shown. The portrait now shows Bella slightly more in the forefront of the photo and with her hand resting on her cheek. 2 or 3 seconds later, Poirot turns the photograph around to its backside and we see that the front has again changed to the first style.
At the first train arrival, the public announcement says (in French) "Attention à la fermeture des portières" which means "Mind closing of doors". This is absurd since passengers are just going off.
In the opening scene, a voice over is being recorded for a Pathé newsreel about the Beroldy case. This scene takes place in 1926, two years before the company's newsreels began using sound.
The first images set the date to MCMXXXII (1932), and we see a steam engine with the SNCF logo (french railways). But the SNCF company (and therefore, its logo) didn't exist before 1938.
At the end of the movie, Hastings bids farewell to Poirot and puts his hands in his pants pocket. As he does this, his jacket lifts up revealing the wire leading to the lapel microphone he is wearing.
In the first time that Poirot, Hastings and Giraud visit Daubreuil's house, when they are leaving, the boom is seen reflected near the car's headlight.