Continuity mistake: At the reception, Miss Euphemia Bouc walks with Miss Van Schuyler and Bowers saying that money is the only friend a woman can rely on. Look at her champagne glass, a little more than half full. Her son jumps on the desk of the lobby and nods to her, and her glass filled up some. (00:22:00)
Continuity mistake: Jackie shows Linnet the engagement ring. Gal Gadot in the view from behind puts her hand on her mouth, and the gesture is repeated in the close-up. (00:12:40)
Other mistake: Poirot saves his entire company except his captain - that's what it was stated, although it's unclear how that can be the case since the explosion was massive and left Poirot disfigured and had several other companions close. That's besides the point though, which is; the captain walked into a trip-wire across the bridge, but earlier shots showed the Germans (several of which were waiting on the same side the Belgians come from) retreating in haste, running exactly where the captain walked. The trap would work only if the Germans were waiting on the other side of the river. There was no chance for them to arm the trap during their hasty escape.
Factual error: When Linnet walks to her room never to wake up again, she walks past a newspaper ("Daily Sketch") with the date of Monday, May 17, 1937. Since the cover story is the opening scene in the night club, and the wedding happens exactly six weeks after that scene, the movie has to take place in July at most. However, in the hotel lobby in Aswan, during the introduction of Ms. Van Schuyler and her companion (right after cousin Andrew tells the clerk that "not a soul" must see the telegram), one of the guests is reading issue 700 of the French magazine Candide, which came out only mid-August of the same year. (00:20:30 - 01:00:10)
Factual error: The opening assault of the movie bears the date October 31, 1914. Poirot's squad attacks the Germans using the cover of gas delivered through canisters. The first documented use of poison gas in warfare was in April of the following year by the Germans, but it possible that the Belgians would attack using non-lethal gas, which they employed starting August of the same year. They wouldn't have the gas masks that they are sporting during the assault, though, including a full headed hood designed by Cluny MacPherson in 1915 (worn by one of the extras that wanders behind Poirot as he takes off his respirator). (00:04:10)
Other mistake: In the origin story of Poirot's facial hair, we see the damage on his cheek is massive, well into the cheekbone. His girlfriend says he'll grow a moustache to cover it, and surprisingly, it works - nevermind the fact that scar tissue wouldn't grow hair. When we see the scar without the moustache, while smaller than the initial damage, it still extends into the cheek at the level of the nostrils in a way that the 'stache couldn't seamlessly cover like in the rest of the movie and its prequel.
Factual error: The movie takes place in 1937: the new and improved Salome Otterbourne of this version has a repertoire of blues songs that are a few years posterior to that date, many years if we count the Rosetta Tharpe versions actually used in the movie. An argument can be made that they are all 'live performances' from a fictional character regardless of the vocalist who actually performed, and so the only song truly 'impossible' in 1937 would be "Shout sister shout", written in 1941, but we don't actually see Salome sing it. She does perform "Up Above My Head" and no recorded version of it exist before 1941, but it comes from a traditional gospel song.