Continuity: When Carr Gomm first meets John, he walks close up to him. In the next shot he is way back from him, then close again.
Continuity: In nearly every scene, John Hurt's make-up changes in some way.
Miscellaneous: First, the nurses say that the Elephant Man must not see any mirror. In the next scene, when the doctor invites Merrick to his house, he has a great mirror there, but Merrick doesn't look at it.