Continuity mistake: Whale commits suicide by drowning himself in the pool. When Clayton pulls him out the color of Whale's suit changes from black to brownish, and vice versa when Clayton throws him back in. Varying degrees of wetness should not be the reason as he should be drenched too while he is lying at the poolside.
Factual error: The supposedly Great War vintage gas mask James Whale finds and later gets Clayton to wear is in fact a British style introduced in the 1930's, and the specific variation shown was not made except during WW2. In addition, during the flashbacks to WW1, various pieces of WW2 equipment crop up (e.g. helmets with spring-loaded canvas covered chin straps instead of leather chin straps, and WW2 British pattern gas mask bags).
Continuity mistake: When Whale and Clayton smoke cigars after lunch you can tell from the ashes at the tip that Clayton's has burned for at least five minutes the very moment after it was lit, while Whale doesn't get his cigar burning properly throughout the scene (which would be a real shame for an obvious cigar aficionado).
Revealing mistake: After Whale compliments Clayton for the marvellous shape of his head, Clayton pulls faces at himself in the side mirror of his pick-up before he drives off. Considering that the camera is positioned at hip level and we see his face in the mirror he couldn't actually see himself.
Continuity mistake: When young Mr. Kay is interviewing James Whale at the poolside Hanna brings some ice tea and two glasses on a tray. She puts the tray down and lays out the place mats. Then she reaches for the first glass, and when she puts it down in front of Kay the other glass is already standing in front of Whale.