Continuity mistake: When Rei is impaled in the chair, the amount of blood on her clothes changes. Blood all over her right arm vanishes by the end.
Visible crew/equipment: In many shots which pan around people, the camera casts a shadow on them, eg. during the sex scene.
Revealing mistake: When the blade swings down into the side of Mako's face, the blood flows down from the top of the blade, and not from her face.
Continuity mistake: When the second spike impales Rei in the chair, the sheets of paper on the floor move further away from the spike between shots.