Continuity mistake: When Zod launches Boog through the cafe window, he lands a couple meters away from the cop, but a shot later he's at his feet.
Visible crew/equipment: When the villains enter the fortress, the moving shadow of the crane used to make them fly is visible when the last villain flies towards the upper left quadrant.
Revealing mistake: When Ursa throws the sewer lid at Superman a sticky object protrudes from his back, revealing the mechanism that pulled him backwards.
Other mistake: When the elevator explodes there's a shot of the Phantom Zone and Ursa is a totally different actress. Different to the other unknown actress used on the first movie, which is also listed as a mistake.
Continuity mistake: After Superman holds the antenna falling on the woman's pram, in a matter of 3 seconds the parked cars she was standing in between (a yellow cab and a black car) come much closer together.
Continuity mistake: In the diner, whilst Clark is asking the bad guy to step outside, the waiter is leaning over the baddie's right shoulder. When the angle changes he is leaning on the left shoulder.
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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