Watson, Holmes. Freud and the Orient Express line all refer to the train destination as Istanbul. However, Continental usage and railroad usage would have used the formal name "Constantinople" until the fall of the Ottoman Empire. Previously, although it had been referred to as Istanbul by locals, it was an informal name meaning "the city." It would never have been used thus by Holmes, Watson, Freud or the railroad.
Freud accuses Holmes of being "egocentric." However, the use of the term ego (Latin for "I") was not used by Freud until the 1920 and the psychological adjective "egocentricity" did not exist until after Freud established the concept of the ego, id and superego in his paper "The Ego and the Id" in 1923.
Holmes tries to follow the man who debarks from the Pasha's carriage. He is rebuffed by guards and says "Saved from a profanation, Watson." However, Holmes can be seen speaking after that with no associated sound.
During the railroad pursuit, the trains are seen on two tracks that are about to merge. Holmes states that there are no points left to switch. However, the coming together of the two track lines necessarily involves a switching point. And, in fact, that set of points is visible soon thereafter.
The goof items below may give away important plot points.
After escaping the horses, Holmes & the others return to the hospital room, where the open door can be seen in the background. After Freud leaves, Holmes sees a lily in the doorway which wasn't there before.
Homes sends Freud to fetch Toby & the revolver. When next they meet, Freud doesn't have Toby because he says he figured out where to look for the lady as he was leaving the hospital. But he has the revolver.
Watson & Holmes encounter the Amin Pasha on their journey to meet Freud. But the plot hinges on him having already been in either Vienna or Monte Carlo days before they arrived there. Their trains would not have met outside Vienna.