Continuity mistake: When Poirot and Mr. Ratchett first meet in the restaurant car, Poirot has to correct Ratchett's pronunciation of his name. Poirot then points with his right hand toward Ratchett, but when it cuts to a close-up of Poirot, both his hands are on the table. The angle changes back, and Poirot's hand is once again lifted.
Continuity mistake: Hercule Poirot takes the German maid to her cabin to look for photographs. She removes her suitcase from the shelf and opens it, showing a very obvious shot of a porter's tunic with many very shiny buttons and space for the missing button (evidence found earlier by Lauren Bacall). The shot cuts away and then immediately back, by which time a porter's hat has appeared on top of the tunic covering all of the buttons previously in shot.
Continuity mistake: In one of the flashback scenes, as the drugs start working on Mr. Ratchett, in a close-up he is holding the last anonymous letter in both hands. Ratchett then removes his glasses with his right hand, and places that hand on his forehead. Back to a close-up of the letter and the letter is in both hands, but when it cuts he is holding the letter with only his left hand again.
Continuity mistake: While it is fairly obvious that many of the flashback scenes are not the same as the original scenes one in particular stands out: during McQueen's second interrogation he describes Mrs Armstrong as being "gentle and frightened" while in the flashback he says "shallow and frightened".