Revealing mistake: When Ursa kicks the astronaut into space, she takes a step back and looks upwards. When this happens you can tell that the film is being shown at double speed. Also, when Clark spins the guy on the chair at the end of the film, he snaps back upright far too quickly.
Continuity mistake: When Zod throws the shotgun after discharging it, it lands in front of the police car's back tyre. But when the dumb one goes to pick the gun up, it is now towards the back of the car.