Other mistake: It's not possible for Holmes to remove all of his elderly bookkeeper disguise in the mere seconds Watson turned his back.
Revealing mistake: While Holmes and Watson are investigating the crime scene, there is a shot of them that shows the dead man's hand. His hand is visibly shaking, revealing the actor is struggling to maintain the position of his hand.
Factual error: Holmes and Watson walks through a colonnade. Clearly visible in the background right over Watson's head is part of a 20th century circular red and white road sign. (00:34:18)