Continuity mistake: In the balloon, after Luthor says "Due North", Teschmaker's arm swaps from raised to lowered.
Revealing mistake: When Luthor is about to climb up the balloon his bald cap wrinkles by his nape.
Revealing mistake: In the prison laundry, Luthor's bald cap is very noticeable, especially by his sideburns.
Continuity mistake: When Lois is cutting oranges the glass jumps from being on the right side of the table to being on the far left.
Continuity mistake: When Superman is crossing the street and a taxi crashes against him, the passers-by are not continuous between shots. Check the African American girl in a pink dress who appears randomly on every single corner of the streets around.
Revealing mistake: When the phantom zone explodes it is a cheap pencil drawing animation.
Continuity mistake: After Lois asks the Paris spokesperson about the bomb he turns around and talks to her. Then it suddenly cuts to a closeup of his face and he's now talking to the journalists that were on the left, without having turned his head or body.
Continuity mistake: At the Eiffel Tower Lois approaches the spokesperson, cut to a wide angle where he is facing left. Then as she arrives there's a close up of him turning around. Then back to the previous wide angle where he is facing left again.
Continuity mistake: Perry White is telling Clark about the terrorists while composing the headlines. Note the cut-out of the word IN under Paris. It swaps from straight to slanted between angles.
Audio problem: In the prison, Lex tells an inmate he wants his Liberace record, to which he replies, "It has a scratch on it," but his lips don't match the audio. In the Donner version, it's revealed that the original audio was "Tonight?"
Continuity mistake: At the Fortress, when Lois drinks champagne, she holds the glass at chest level. A shot later, her arm is lowered.
Revealing mistake: When Non flies through the White House ceiling, right before he lands on his feet, the shot cuts to Zod landing safely and one can see that the previous stuntman missed the landing and fell on his back, his legs now pointing upwards. According to the shooting script and the additional Donner scenes, the fall was not scripted and not plot-wise.
Revealing mistake: When Superman returns the flag, the wide shots show he has really long arms and a brown blob where the head should be, revealing the actor has been replaced with a dummy.
Continuity mistake: Right before Perry White throws a bronze globe at Non, Lois' head is tilted sideways and she smiles calmly. An instant cut later, her head is straight and she stares in awe. After the globe strikes Non's head, we're back to the previous shot where her head is tilted.
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: 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.
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.
Continuity mistake: Inside the White House the cops fire 3 or 4 times at Zod but the wall and statue behind him have at least 15 bullet holes.
Other mistake: When the elevator explodes there's a shot of the Phantom Zone and Ursa is a totally different actress. Different to the other unknown actress used on the first movie, which is also listed as a mistake.
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