Continuity mistake: When Superman is putting the antenna back in place, watch the right of the platform with a bunch of metal parts and cables sparking. In the closeup they disappear.
Continuity mistake: Inside the White House the cops fire 3 or 4 times at Zod but the wall and statue behind him have at least 15 bullet holes.
Continuity mistake: The branch that Superman cuts to save Lois from drowning swaps from bright milky chocolate colour to pale dark brown depending on the shot.
Continuity mistake: In the balloon, after Luthor says "Due North", Teschmaker's arm swaps from raised to lowered.
Revealing mistake: When Luthor is about to climb up the balloon his bald cap wrinkles by his nape.
Revealing mistake: In the prison laundry, Luthor's bald cap is very noticeable, especially by his sideburns.
Continuity mistake: When Lois is cutting oranges the glass jumps from being on the right side of the table to being on the far left.
Continuity mistake: When Superman is crossing the street and a taxi crashes against him, the passers-by are not continuous between shots. Check the African American girl in a pink dress who appears randomly on every single corner of the streets around.
Revealing mistake: When the phantom zone explodes it is a cheap pencil drawing animation.
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 Lois asks the Paris spokesperson about the bomb he turns around and talks to her. Then it suddenly cuts to a closeup of his face and he's now talking to the journalists that were on the left, without having turned his head or body.
Continuity mistake: At the Eiffel Tower Lois approaches the spokesperson, cut to a wide angle where he is facing left. Then as she arrives there's a close up of him turning around. Then back to the previous wide angle where he is facing left again.
Other mistake: The phantom zone villains were captured and put in space near Krypton. When Kal-El was sent to Earth, he has to pass 6 galaxies to arrive (his father said, before Krypton exploded). When Superman sends the hydrogen bomb in Paris into space, he didn't even leave the solar system. No way the phantom zone travelled through 6 galaxies - it has no propulsion, and the shock wave from the bomb wouldn't travel that far either.
Continuity mistake: Perry White is telling Clark about the terrorists while composing the headlines. Note the cut-out of the word IN under Paris. It swaps from straight to slanted between angles.
Revealing mistake: When Luthor and Teschmaker are in the balloon, in the wide angle they both become coloured green due to the blue screen effect.
Visible crew/equipment: There is a moving boom mic above Clark when he talks to Mr. White about the terrorists in Paris. (The Ultimate Collector´s Edition Box Set).
Revealing mistake: When Superman launches the Eiffel elevator in space and he flies back to earth, a white rectangle surrounds him where his image was superimposed to achieve the flying effects. (The Ultimate Collector´s Edition Box Set).
Visible crew/equipment: Stage lights are reflected on the orange squeezer at the start of the movie.
Continuity mistake: During the fight in Metropolis, Zod throws a concrete wall which Superman explodes. When debris falls, a taxi stops but a grey car behind keeps moving. In the close-up the grey car is parked several meters behind the yellow one.
Revealing mistake: When Superman grabs the antenna above the pram, part of the antenna disappears because of the blue screen effects.
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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