Continuity mistake: During the big sex scene you see red marks on Michael Douglas's back. These red marks are from when Sharon Stone scratches him. The thing is, she scratches him a minute AFTER you see the red marks on him for the first time.
Continuity mistake: During the interrogation scene, Stone has her legs crossed right over the left then suddenly left over the right and a second later (during the shot where she wears no underwear) right to left again.
Trivia: Director Paul Verhoeven actually has a PhD in mathematics. He received it back in the 1960's in Holland. He left the field and became a film director. (From Director's commentary on "BasicInstinct: The Original Director's Cut".).