Other mistake: When Lois and Clark leave the Fortress, the car is driving in the wrong lane. This is due to the fact that the shot belongs to a reused scene from the first movie, where an empty car was remotely driven by Lex, who changed lanes all the time.
Other mistake: When Clark and Lois are on their way to the diner, the wide shot of their car driving along looked very familiar. In fact, it was footage used in the first movie, where the car was used as part of Lex Luthor's "real-estate" plan and was run on remote control. If you look closely in part II, no one is driving the car yet you hear Clark say to Lois, "Hey, you seem pretty quiet over there...."
Other mistake: At the end of the film Superman puts the US flag back onto the Whitehouse. Whilst he is speaking to the President through the hole in the roof the flag can clearly be seen flying in the wind, but his cape is completely still.
Other mistake: When Ursa, Non and Zod first arrive on earth, watch out for the horrible lipstick marks on Ursa's teeth as they walk away from the lake.
Other mistake: In the long shot of the Niagara Falls scene, the kid's right arm is way too long.
Other mistake: When Clark and Lois return from the Fortress of Solitude in a green car, the footage is the exact same one used in Superman I when Luthor later crashed that very same car (time code for Superman I 1:34:04 vs 1:18:25 for Superman II).
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.
Other mistake: As Lois goes to climb under the lift, the one support she climbs over is bowed down a bit, whereas the others are straight, as if there were more than one take done.
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.
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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