Revealing mistake: In the scene where Det. Mills is chasing John Doe through the streets they end up in an alley, and Doe knocks Mills down with a crowbar. As Somerset runs up, Doe runs off and Mills drops back down to the ground and rolls off his side onto his stomach. As he does so you can see a red colored tube running from the back of his jacket/collar, across the back of his head to his forehead, supplying "blood".
Revealing mistake: Sloth is shown with three "arms." It's most easily noticed after he wakes up. His right arm is bent at the elbow, pointing to the ceiling, his left arm is pressed tightly to his left side between his torso and the jacket used to conceal the upper part of the prosthesis, and his third "arm", the prosthesis, is bent at the elbow, hanging halfway off the bed, and pointing to the left of his body. It has several large, protruding "veins" in it and the stump where the hand should be is off-screen.