Factual error: Before arriving at Brod station the train goes through high mountains. Between Belgrade (Serbia) and Brod (Bosnia and Croatia) it is all flat with no mountains around.
Factual error: At beginning at the Wailing Wall in Jerusalem in 1936, we see the large plaza at the Western Wall. In 1936 this was only a narrow lane. The plaza was enlarged only after June 1967.
Factual error: When facing the western wall, Poirot orders a man to guard the south gate. The man runs to the left of the frame. The western wall is what remains of the old temple, which lay to the east of the current plaza, so when you're standing looking at the wall you're actually facing east, not west. The man runs the wrong way.
Factual error: In the breakfast scene involving eggs, Poirot refers correctly in French to one egg "un oeuf" (pronounced "erf"). However, Branagh mispronounces the plural. He said "oeufs" ("erfs"). The correct pronounciation omits the f and the s, correctly sounding like "euhh." Poirot is French-speaking so would know better.
Factual error: Poirot refers to the senior police officer in Jerusalem as the Chief Inspector of Police and implies that he commands the police in Jerusalem. The Palestine Police had no rank of Chief Inspector. The three stars worn by the officer were the insignia of an Assistant Superintendent of Police, the entry-level rank for gazetted officers. The head of the Jerusalem police was a District Superintendent of Police, two ranks higher. As Poirot is famously a stickler for detail, it's certainly not a character mistake.
Factual error: The Orient Express had a restaurant coach, four sleeping coaches and two baggage cars, and carried 58 passengers, far larger than the train depicted. There was a conductor always on duty in every sleeping coach and they worked shifts, so more than four would be carried; it's stated that Michel is the only conductor on board.
Factual error: When the steam engine is derailed and is surrounded by snow from the avalanche, there would be a high risk of the boiler and/or firebox overheating. Under these circumstances, the driver would "drop the fire" by opening the bottom of the firebox to drop the coals onto the track. This would cause delay in restarting the train, so the passengers would be taken to safety and warmth by a rescue train.