Continuity mistake: When Lois is making an orange juice the position of the oranges differs between wide and close shots.
Continuity mistake: During the scene where villains arrive to the Daily Planet, Jimmy Olsen's haircut changes from long to very short.
Continuity mistake: When Clark comes back to the diner to take revenge, a dish next to the bad guy suddenly appears.
Continuity mistake: When Super arrives at the Daily Planet to defy the 3 villains, the outside shot shows three piles of books lined along the window. From the inside, all of the books are piled to the right. Also, the number of trophies on the bookshelf on the right, and the type and number of books changes between shots.
Continuity mistake: At the end of the movie, in the diner, the bad guy's food keeps changing appearance.
Continuity mistake: When Superman reveals his identity to Lois, the liquid in the top of the lava lamp changes from filled to empty in half a second.
Visible crew/equipment: Crew members are seen wandering inside Lois' apartment at the end of the movie.
Revealing mistake: When Non and Zod break in through the White House window, a black strap is seen attached to each one's body to help them descend safely.
Continuity mistake: After Superman throws Zod against the ice wall, Non's position changes between shots: First he is way behind Luthor, and a second later both are side by side.
Continuity mistake: When Non enters the Daily Planet there's a wood shelf with four sheets of paper, the ones in the middle are yellow and the rest are black and white. When the shot changes to a wide angle, all the papers are black and white.
Revealing mistake: When Zod throws a man against the wall in East Houston, the man goes through the wall into a truck. Before he crashes against the truck, wires holding him are visible.
Continuity mistake: When Ursa sits down to arm wrestle, coasters magically appear on the table.
Continuity mistake: When Non rampages the Daily planet, the grey file cabinet lying on the floor changes positions before and after he enters.
Continuity mistake: Superman descends to stop the big truck from exploding and lands in front of it, by the cabin. A frame later he is seen landing a meter before the truck.
Continuity mistake: When the antenna is about to crush the pram, the mother is first behind it. A second later she's by the side. Then a second later she's on top of it, and a second afterwards slightly covering it. Boy she moves FAST.
Continuity mistake: Inside the Fortress of Solitude, when Non jumps to fight Superman, before he flies, Ursa and Lois are looking at Superman. A mere frame later, when Non starts to fly, both girls are in a different position fighting against each other. It's a really awkward and sudden change.
Continuity mistake: At the end, in the Fortress of Solitude, Lois' hairstyle keeps changing from fluffy and dull to smooth and stylish.
Continuity mistake: After the hide and seek game in the ice cave, Luthor's fringe constantly changes length and style.
Continuity mistake: Clark steps out of the diner and the waiter has his hands on his chest. A shot later his hands are on the counter.
Continuity mistake: After being hit by a cab, Lois calls Clark and the people behind her change in a split second.
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