Other mistake: When Claire Spencer loses her husband's mistress' braid in the lake, she tells him this and Dr. Norman Spencer acts like it's the first time he's heard her talk about it as he picks it out of the water. She has, however, mentioned the braid a short time before this to him, right after the rough sex they've had.
Other mistake: When Claire turns the hot water valve with the chain, it's turned in the wrong direction. It was turned to open it more.
Chosen answer: Spencer's theorem was Norman's father's theorem. Norman wants to be greater than his father was, so to be accidentally complemented on something that his father did would be bad enough. To say that the guy knows that his father is dead is to imply that the guy probably insulted him intentionally.
Myridon