Audio problem: In the Fortress of Solitude, when Superman kneels before Zod, we hear Lois sobbing, but her mouth and body don't move.
Sacha
Deliberate mistake: French officers and firemen speak in English between them.
Sacha Continuity mistake: Inside the bar in East Houston, Zod pushes a man backwards, but the next shot shows the man flying as if he had been thrown upwards.
Sacha Revealing mistake: When Non goes through the pavement, the hole reveals it's a foam made floor.
Sacha 
Visible crew/equipment: When Non crashes Perry against the ceiling, a crew member's hand is seen holding Perry.
Sacha 
Revealing mistake: During the big fight in Metropolis, the close-up of the pram shows its empty. It must a very expensive pram for the mother to protect it in such a heroic way.
Sacha Continuity mistake: When Superman falls on the Marlboro truck, the part reading "Ma" gets more crumpled after Superman leaves the truck compared to when he landed on it.
Sacha Revealing mistake: When there are multiple Superman's in his home, Lois Lane runs to one of the fakes. It seems as if she is the fake because her image becomes slightly transparent as she runs through him.
Revealing mistake: Near the end of the film when the 3 villains enter the fortress, Ursa throws Lex Luther off her back and flies away. You can clearly see that it was a stuntman and not Gene Hackman.
Continuity mistake: When the News Beat reporter arrives, the shadow on the satellite dish changes significantly in a couple of seconds.
Sacha Continuity mistake: When the elevator falls down the shaft with Lois trapped underneath, Superman flies up to rescue her. He stops the elevator, and when he does, Lois climbs off from the bottom of the elevator and runs to hug him. Problem is, when she climbed off the bottom of the elevator, there should have been nothing but air underneath her.
K.C. SierraContinuity mistake: While in the water, Lois grabs the log with her right hand. A shot later she is away from the log and she grabs it again, though now she uses her left hand.
Sacha 
Revealing mistake: When Lois jumps in the river, she is replaced by a very obvious mannequin that floats stiff. Furthermore, the current tilts the dummy and its two arms bent like a sex doll's are perfectly visible.
Sacha Continuity mistake: After Zod launches Boog through the truck the cop asks if he's OK and he and the kid turn sideways an look at him. A shot later they are facing straight.
Sacha 
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.
Sacha Revealing mistake: When Superman arrives at the tropical place, the sea doesn't move, revealing it's a very obvious still picture where a flying Superman has been inserted.
Sacha Revealing mistake: After the army jeep drives through a House in East Houston, notice the driver's stiffness despite the crash and fall, revealing it's a dummy.
Sacha Revealing mistake: When the 3 villains start blowing at the people in Metropolis, the papers come blowing from the left and right sides of the set, revealing where the huge fans where placed to achieve the effect.
Sacha 
Revealing mistake: When Ursa throws the sewer lid at Superman a sticky object protrudes from his back, revealing the mechanism that pulled him backwards.
Sacha Audio problem: During the disappearing/reappearing scene, Superman grabs Zod's neck and cries "Wrong again, Zod!" but his mouth isn't moving.
Sacha 
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