Continuity mistake: When doctor Nemur, that other doctor, and Mrs. Kinnian are discussing possible complications with Charlie's surgery, there's one shot where Dr. Nemur takes the cigarette out of his mouth and in the next shot it's back in.
Revealing mistake: Whenever Dr. Nemur is smoking, you can tell the cigarette's not lit, because you can't see any smoke. When Mrs. Kinnian smokes in the movie, plenty of smoke is visible.
Factual error: There's one scene where Charly's just woken up from his surgery. The next scene shows him working on a puzzle, and he has a full head of hair and no bandages. If he'd just got brain surgery, don't you think he'd still be wearing bandages or at least have his head shaved?