Continuity mistake: When Ursa says to the Cosmonaut "What kind of creature are you?" her whole body is facing forward. He responds "Just a man" and in the next shot of her, her body has turned left. Then when she goes to grab his patch her body is facing forward again.
Other mistake: The cab that slammed into Clark earlier in the film is seen coming around a corner during the confrontation. The amount of damage inflicted from running into the equivalent of a thick concrete pole should have rendered it inoperable, as the radiator was pushed back into the engine. Even if repaired, the front would have been repaired as well.
Continuity mistake: The kid fell backwards off the ledge and down toward the falls, but the distance shot he's face down rather than face up. It's also easy to see that it's a dummy because the hair color is different, as well as the body structure and limb movements are all wrong for a human.
Continuity mistake: During the Marlboro truck scene, a woman with a violet dress and curly hair is inside her car laughing at the fight. This lady appears in almost every single angle of the flying sewers scene with no continuity at all: sometimes standing, sometimes falling, other times somewhere opposite to where she was before.
Continuity mistake: Right after Ursa cries "Superman" and is about to throw the sewer lid at him, a man with a white jacket and a big afro runs from right to left and hides behind her. When the angle changes, he is on the very far right side of the street, many meters away, running towards Ursa, repeating all previous movements.