Visible crew/equipment: When Lois pulls up to the house where the blackout was traced to, she hears some music coming from the boat down at the dock. As the camera pans upwards over the car, as she steps out, the whole camera and a crew member are reflected in the side of the car.
Visible crew/equipment: In the scene where Martha Kent investigates the crystal ship, there is a fuzzy outline of a crew member behind the truck.
Answer: The film doesn't take place between II and III, it just carries on from Superman II, ignoring 3 and 4 completely. Think of it as a parallel timeline.
Tailkinker ★