Audio problem: When Superman falls from the sky due to being exposed to the Kryptonite, he is heard screaming but his mouth never moves or opens as this happens. (00:55:20)
Continuity mistake: The second time we see Superman and Batman go into Lex's elevator, Superman and Batman have some distance between them. It cuts to a shot inside the elevator and they are suddenly much closer. (00:50:00)
Trivia: When The Joker interrupts the ceremony and shows the video of him blowing up the building, there's a scene where he hits the detonator a few times before the building blows up. This is a scene paying homage to what happened in The Dark Knight when there was an actual unplanned delay during filming of the explosion going off during the blowing up of the hospital.