Continuity mistake: At a meeting to do with the hospital's dealings, one man, Mr Broadbeck, objects to the Elephant Man being a patient in the hospital - in the beginning he is wearing spectacles, but, a few seconds later, the spectacles are gone.
Deliberate mistake: Joseph (John) Merrick's speech was never as audible as shown in the film, and several operations were needed before he could speak at all. Even after that, Frederick Treves often had to "translate" what Merrick said because the majority of people still had problems understanding him. [Probably changed to simplify the storytelling, but still inaccurate].
Continuity mistake: The period of time this movie portrays about Merrick, was in real life a period of seven years. In real life, Merrick's deformations were not so 'big' at 21, and at the date of dying, they were larger than portrayed in the movie. In the movie his deformations never seem to enlarge.
Continuity mistake: When Treeves is interrupted taking a plate of food up to John by Sir John Gielguld, Treeves hides the bowl of food behind his back. In the next shot the bowl is still in front of him; then once again he attempts to hide the bowl of food behind his back.