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.
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.
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: During the Metropolis battle, after Non and Super go down through the pavement, Non is launched upwards thorough the concrete. Check the people around, specially the cop on the right. They are blatant toys (note the cop's weird arms), revealing it is all a miniature set.
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.
Continuity mistake: In Krypton when Non breaks the guard's neck the guard presses an emergency button. In the wide angle all of his fingers are extended, but in the close-up only the index is. This changes back and forth.
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.
Audio problem: When Ursa lifts the bus she mumbles and laughs, but her mouth is closed.
Audio problem: When Non is launched towards the Empire State a man says "Wow, home run!", but his lips are not in sync.
Revealing mistake: When Non punches Superman and he crashes against a metal wall, there's a brief shot where Chris Reeve's stunt double is very noticeable.
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.
Continuity mistake: At the Fortress, when the 3 villains extend their arms to send a laser beam to Superman, there's a very brief shot on Ursa and her hair style is completely different. Very short and with her forehead very clear.
Answer: In the theatrical cut, nobody really knows why the green crystal restored his powers. However if you watch the Richard Donner cut, it is explained that the green crystal is a communication device that helps Superman talks to the residual essence/spirit/ghost of his father Jor-El. Before he died, Jor-El gave the crystal to his son. Jor-El anticipated that Kal-El might give up his powers, and he also anticipated that Zod might eventually escape the Phantom Zone, so Jor-El lets his son absorb the leftover energy of his spirit, thus restoring all his Kryptonian powers.
Matt Van Gogh