Factual error: The colt .45 that Telly Savalas uses didn't come into use until 1911 (the film's set in 1909).
Continuity mistake: Several characters say that the train leaves from Shanghai. But the caption at the beginning says that the starting location is Peking (which is in fact where the real Trans-Siberian Express did depart from).
Factual error: When the monk is looking through the microscope, the train goes through a tunnel and the car goes dark, but since the scene is at night and the car was already lit a tunnel shouldn't have made any difference.