Revealing mistake: Right when the Metropolis fight is about to start, Superman flies to the Daily Planet and passes by a building. Check the pattern on the windows and you'll notice that the same small door on the left appears almost everywhere, revealing that a miniature was used.
Revealing mistake: The villains send cars flying through the air. This was achieved with detailed scale model cars in a scale model Metropolis. But in order to mimic the blown-away citizens they use cheap mannequins that move on some sort of conveyor belt. (01:43:50)
Revealing mistake: When the villains blow away the stuff in Metropolis, the fire hydrant falls down and reveals it wasn't fixed to the ground, a blatant prop.
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.
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.
Revealing mistake: When the phantom zone explodes it is a cheap pencil drawing animation.
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.
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).
Revealing mistake: When Superman grabs the antenna above the pram, part of the antenna disappears because of the blue screen effects.
Revealing mistake: As Zod and crew blow people and objects down the street, it is obvious in some shots that they're all heading toward a painted studio wall.
Revealing mistake: As Ursa slams the man's arm down, the section of the table their arms hit has been cut to make the stunt possible.
Revealing mistake: As Non lifts the car to get the shotgun, the front of the undercarriage has a pile of dirt it, possibly to hide the lifting device.
Revealing mistake: The Cosmonaut Zod meets first pulls at his supply line. As he does, if you look closely the black wire used to make the hose move is visible.
Revealing mistake: As the astronaut that Ursa meets moves, the wires used to make him float are visible.
Revealing mistake: In a close-up shot of the kid falling into the falls, one can notice the kid is just a dummy. Notice how his face is a lot paler than it was before. (00:39:35)
Revealing mistake: The hole that Non and Superman go through is already patched, as it's a different colour from the rest of the pavement (either from previous takes or to allow the effect).
Revealing mistake: During the Marlboro truck scene, Zod's stunt double has very noticeably longer, darker and bulkier hair, plus a thicker beard.
Revealing mistake: After coming out of the Marlboro truck, Superman grabs Zod by his feet. When he sends him flying away, Zod's been replaced by an obvious doll.
Revealing mistake: In the first scene when the villains are at the console, you can see Ursa's nose disappear, then reappear when Non walks behind her, then it disappears again. (01:44:30)
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.
Matty Blast