Episode #1.1 - S1-E1
Continuity mistake: When he is asked "The culprit is a woman, isn't it?", the doctor is suddenly holding the pen between both hands instead of just with the right hand. (00:29:55)
Episode #1.1 - S1-E1
Factual error: The series is set in 1933, as the initial captions show. Yet the locomotive pulling the Orient Express is a JNR Class C58: the C58 series was built starting from 1938 (C58 239 used here is from 1940).
Episode #1.2 - S1-E2
Plot hole: Contrary to any other version (including the novel), here the mastermind behind the murder realises in timely fashion that burning the letter was a mistake, it was not actually part of the plan. With this change, they'd have still all the time in the world to go back to the compartment and get the burnt remains, but they simply do not.
Episode #1.2 - S1-E2
Continuity mistake: When the equivalent of Miss Debenham tells the Colonel that reaching the 12 people figure might be difficult, her hands and the secretarys are in a different position compared to the previous shot (hers are raised, his are crossed in a different pattern). (00:45:45)