Factual error: After Superman accidentally frees the phantom zone villains with the exploding hydrogen bomb, they start flying towards the moon. The sleeves in their clothes can be seen fluttering around. This would be impossible because there is no air in outer space, hence nothing to cause resistance against the clothes.
Factual error: The moon has no atmosphere. Yet, the Ursa and Zod are able to speak to the astronauts. We even hear wind as Zod kicks one of the astronauts in the air and snaps his cord. We also hear the explosions when the lunar lander is destroyed. If the moon has no atmosphere, then the super villains can't speak and there should have been no sound in this part of the movie.
Factual error: When the police car's light is thrown at the boy and it blows up, it shouldn't have happened. The most that would've happened was that the kid would've been knocked off his bike when hit with the light. There is no explosive device in the light, so it shouldn't have exploded in the least like it did.
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