Continuity mistake: In the first scene, when the guard gets caught off-guard by Non his right arm is on the side, in the close up it is bent to defend against Non. A frame later it's down.
Continuity mistake: After crushing Zod's hand, Superman sends him flying away. Luthor's head turns around twice.
Revealing mistake: When Non falls on Superman and breaks the concrete, the hole opens before Non falls on him.
Continuity mistake: When the ring falls on the villains, Non is looking down and a split second later he is looking up.
Revealing mistake: When Non goes through the pavement, the hole reveals it's a foam made floor.
Revealing mistake: In the ice cave, when Superman makes himself invisible, watch Zod's head jumping slightly to the back, revealing where the scene was edited to achieve the effect.
Continuity mistake: When Non is about to break Perry's desk in half, Jimmy and Lois are standing very close to each other. A split second later they're farther apart.
Revealing mistake: In the ice cave, Superman throws a plastic S at Non. The wires moving it are visible.
Visible crew/equipment: When Non crashes Perry against the ceiling, a crew member's hand is seen holding Perry.
Continuity mistake: When Lois prepares orange juice, Clark lowers his left arm and sneaks it behind his back. A second later the arm is up.
Revealing mistake: During the big fight in Metropolis, the close-up of the pram shows its empty or with blatant bundled pieces of fabric to simulate some sort of baby.
Continuity mistake: When Superman falls on the Marlboro truck, the part reading "Ma" gets more crumpled after Superman leaves the truck compared to when he landed on it.
Continuity mistake: Zod makes a short jump from the white car to the Marlboro truck, but in the next shot we see the two cars are several feet further apart.
Continuity mistake: In East Houston, the army jeep is passing by a brown car, then Ursa talks and we hear the jeep engine coming close, but when the image focuses back on the jeep it is several feet behind the brown car, instead of being in front of it.
Visible crew/equipment: Wires holding Superman are visible when he is about to stop the elevator.
Continuity mistake: In East Houston, while the helicopter fires at the 3 villains, a soldier runs behind Ursa and she is left totally alone. In the next shot he is behind her, running away again.
Continuity mistake: When Clark crosses the street before being hit by a cab there's barely no people behind, in the next shot there's a lot more.
Continuity mistake: When Clark comes out of the river one shot shows the back of his jacket with one half up and another down. When the angle changes the entire jacket is up.
Revealing mistake: When the Empire State antenna falls down the wires holding it are visible.
Audio problem: Most of the times when the French terrorists talk, their lips are not in synch or their mouths don't move.
Answer: Superman was be able to kiss Lois in such a way that the heightened emotion wiped out her memory of his identity. To answer your second question, even though Lois promised not to tell anyone, Superman decided he does not want even her to know his secret identity.
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