Continuity mistake: In the plane, after Superman says that planes are safe, the man next to Lois raises his arm way up high, but a frame later, from an angle behind, he is barely raising the tip of his hand.
Continuity mistake: When Lois and Clark exit the building and she scolds him for leaving, the passers by don't match between one shot and the other.
Continuity mistake: A tube and oxygen mask suddenly appear over the seat in front of Lois after Superman enters the plane.
Continuity mistake: Clark's dog leaves a baseball on the ground and walks until being parallel to Clark's both legs. A frame later the dog is two meters behind, next to Clark's left knee.
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 ★