Revealing mistake: At the Fortress, when the villains and Superman play the appearing/disappearing trick, there's a shot with 4 Supermen onscreen, a special effect which was achieved with stand-ins. The one in front of Zod, and especially the one next to Lois look nothing like Christopher Reeve.
Continuity mistake: At the Fortress, when the 3 villains extend their arms to send a laser beam to Superman, there's a very brief shot on Ursa and her hair style is completely different. Very short and with her forehead very clear.
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: 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.
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.
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.
Other mistake: When the three villains jump out of the Daily Planet window they just break some glass; however, from a ground level shot huge chunks of concrete are falling. This is more dramatic, indeed, but senseless.
Revealing mistake: During the Metropolis battle, after Non and Super go down through the pavement, Non is launched upwards thorough the concrete. Check the people around, specially the cop on the right. They are blatant toys (note the cop's weird arms), revealing it is all a miniature set.
Audio problem: When Non is launched towards the Empire State a man says "Wow, home run!", but his lips are not in sync.
Revealing mistake: When Non punches Superman and he crashes against a metal wall, there's a brief shot where Chris Reeve's stunt double is very noticeable.
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.
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.
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.
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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