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.

Continuity mistake: The writings on the note Lois faxes to the Daily Planet (with the coordinates) change from when she writes it to when Jimmy sees it through his camera. For example, the 'N' is much smaller and the 'P' is fatter in the faxed version. (01:31:45)
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: After the plane has landed in the stadium and Superman is checking if the passengers are all okay, note the speaker's glasses. They alternate between being very crooked to being perfectly straight. (00:41:15)
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 ★