Continuity mistake: When Zod is interviewed by the news reporter the people behind him differ or change positions between shots.
Continuity mistake: When Lois comes out of the river she turns to the left to help Clark. Shot changes and she has turned 180ยบ around.
Revealing mistake: When Superman returns the flag to the White House, not only has the shot been reused, but the trees have been badly cut around to change the previous grey sky for a bright, blue and sunny one.
Revealing mistake: When Non burns the side of the cargo bed of the truck, a rectangular spot around the planks is coloured in a lighter shade, giving away where the special FX were placed.
Revealing mistake: When the villains enter the oval office, the whole White House behind is a cheap set with painted columns, furniture, fixtures and switches (even the bullet holes are painted!). (01:16:29)
Revealing mistake: When Superman flies towards the White House, in the close-up his cape and flag flutter at a normal speed, but in the wide shot they move really fast, quite comically actually, revealing that the scene has been speeded-up.
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).
Continuity 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.
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.
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.
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.
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.
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.
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.
Revealing mistake: When Ursa throws the sewer lid at Superman a sticky object protrudes from his back, revealing the mechanism that pulled him backwards.
Audio problem: During the disappearing/reappearing scene, Superman grabs Zod's neck and cries "Wrong again, Zod!" but his mouth isn't moving.
Visible crew/equipment: When the villains enter the fortress, the moving shadow of the crane used to make them fly is visible when the last villain flies towards the upper left quadrant.
Continuity mistake: When the movie begins Zod breaks the red glass and there's a brief shot of Ursa looking in fear. Her hair is longer than in the previous shot.
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.
Continuity mistake: When the villains are trapped in the phantom zone (filmed by Richard Donner) Zod, Non and Ursa (from left to right) are tightly pressed against a glass. When the elevator explodes and are about to be released (filmed by Richard Lester) not only are they not pressed, but neither in line, having changed positions (and looks, as already listed): Non now stands above Zod and Ursa.
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