In Superman (1978) and Superman II (1980) Lex Luthor wears a wig because he is completely bald. In this film, Lex is balding (as Gene Hackman was in real life).
During the fight on the moon, one shot shows what appears to be the US flag torn/tattered. Two minutes later Superman re-stands the flag and it is now clean and fully intact.
(at around 1h 15 mins) Lex Luthor's hideout is supposed to be at the top of the "Metropolis State Building" (stated in the deleted scene of the creation of the 1st Nuclear Man, in the Special Features section of the DVD). When Nuclear Man crashes through the floor to find Lacy Warfield, not only are he and Superman supposed to be in a different building (the canopy outside says "Metropolis Tower"), but the room is clearly the set for Lex Luthor's lair.
(at around 1h 3 mins) When Nuclear Man flies over a street full of people, threatening to drop the Statue of Liberty on them, the crowd looks up in horror and screams. In the next shot, the street contains moving traffic, and no people. In the next shot, the people are visible again.
(at around 54 mins) When Clark Kent is looking out of the window of Laci's kitchen after he hears the message from Lex, the billboard beneath the one where Lex's picture appears clearly says "Super Slurpee". When the camera moves closer to the screen in the shot, the billboard has a completely different ad on it.
(at around 1h 20 mins) Lacy Warfield is able to survive in space without a space suit.
(at around 32 mins) At the United Nations, the nation immediately to the left of the aisle is "England". "England" is not a member of the United Nations, "The United Kingdom" is a member of the United Nations.
(at around 1h 1 min) To stop the eruption of Mt. Vesuvius, Superman is shown plugging up the volcano with the top of a mountain. While this would temporarily cease the eruption, the pressure inside the volcano would keep building and building until the entire volcano explodes which would be a far more devastating, costly, and deadly disaster.
Nuclear Man was created using genetic material harvested from one of Superman's hairs. Lex Luthor get this hair from a museum using bolt cutters. He cuts the top and bottom off to get at the part in the middle. He takes only the middle part with him. Genetic material is only found in the follicle of a hair, which would be at one end.
Capes flap in space and Superman is able to speak to the Cosmonaut, even though there is no air in space.
Superman used up the last energy crystal from his parents in Superman II (1980), but another "last" crystal is mysteriously available for him to use in this movie. In some cuts of Superman II, Superman went back in time (as he did in Superman (1978)) to cancel out many inconvenient plot developments, so this film may follow one of those cuts.
(at around 1h 13 mins) Near the end of the film, Nuclear Man sees the photo of Lacy Warfield and then goes to the Daily Planet to find her. Outside, he meets Superman and asks "where is she?" Superman replies "you'll never find her". Though he never said who he is talking about so that Superman may not have known who he meant, it is plausible that Superman might have assumed he may have meant Lois, since she is the one person he cares about the most.
(at around 28 mins) When Superman is flying with Lois Lane, there is one point where he lets go of her to let her fall so he can catch her. Lois should be falling straight down, but the background indicates that she is still flying. Lois would only fall straight down if she and Superman were stationary in the air, the speed at which Superman is flying when he lets go of her hand would have given Lois enough momentum to keep moving forward while falling, thus it appears that she is still flying.
(at around 1h 20 mins) When Superman pushes the moon out of orbit to stop Nuclear Man, he pushes either black lava rock or black granite. The Moon is gray, unless he was pushing a crater, in which case the ground and hills around it would still be gray.
Parts of the moon are darker than the usual gray, these are commonly known as "mare" (Latin for sea) and have names such as sea of tranquility or sea of clouds etc. These mare are the result of volcanic activity in the past, therefore it is possible for superman to be pushing volcanic rock on the moon.
(at around 1h 17 mins) When Superman and Nuclear Man are fighting on the moon, there is an insert shot of Nuclear Man's foot stamping on Superman's, yet the following mid-shot implies that it was Superman who stamped on Nuclear Man's foot.
While it may appear that this is what happened, Superman is actually kicking Nuclearman's foot upwards, which explains why the latter stumbles. However the close up shot could well have been achieved by rewinding a film of Nuclearman stomping on Superman's foot.
(at around 1h 34 mins) When Superman is flying the Statue of Liberty back to its rightful home, one of the flying shots uses a black and white background plate of New York, where as the rest of the scene and all of the other shots are in full colour.
(at around 1h 13 mins) Nuclear Man crushes in the front of a cab (a Dodge Aspen, which seems to have no engine). In the next shot, a big white string stretches off screen from the cab's TAXI sign, just before the second cab (a Chevrolet Caprice) hits the back of the already-wrecked cab.
(at around 1h 3 mins) In the shot of Superman flying, just before he looks behind him to see the Statue Of Liberty taking off, a red string is holding Superman's cape straight.
(at around 20 mins) When Lex is stealing Superman's hair, the hole for the 1 ton weight to fall through is revealed when the fake flooring on the base falls away too soon.
(at around 41 mins) After the missile with Nuclear Man's DNA attached is launched, Superman races after it. When he grabs the underbelly and they streak out of frame, a small square appears in the bottom left of the screen, showing the scaffolding Christopher Reeve is hanging from (Travelling Matte).
The Fortress of Solitude is shown in this film. Even though, Superman destroyed it with his heat vision in the 2006 Donner cut. However, in that same cut, Superman did also reverse time to long before he destroyed it, which explains why it appears in one piece.
The workers take down the Warfield sign twice .
(at around 4 mins) When Superman is speaking in Russian to the cosmonauts, his voice is obviously dubbed.
Every single time Supes flies left or right, up or down, toward or away from the camera, his cape makes a squeaking sound like it's made of plastic.
When Superman lands on the moon, wires are clearly visible attached to his back, even as he walks on the surface of the moon.
(at around 1h 17 mins) When Superman and Nuclear Man fight on the moon, black curtains appear in the distance in several shots.
(at around 1h 14 mins) When Nuclear Man tips the SWAT van on its grill and spins it around, a SWAT officer flies upwards out of the back. The flying wires connected to the officer are showing.
(at around 1h 15 mins) When Nuclear Man flies through each level of the Daily Planet, the wires pulling him up are clearly visible.
During the final moon battle, wires appear on Superman and Nuclear Man in several frames.
The Daily Planet is supposed to be a U.S. newspaper. One headline uses the British spelling of "favourite." The American spelling has no U.
(at around 1h 24 mins) At the end, the sequence of Lex and Lenny on the 'interstate' includes a white hard shoulder stripe and an orange SOS box, hallmarks of a British motorway. They're actually on the M25.
The trains and the subway system are part the London Underground, not New York's subway system.
(at around 1h 19 mins) When Nuclear Man returns to Earth, the scene with the Moon in the distance shows a view of the Moon that cannot be seen from Earth.
Cars with UK license plates are visible in several shots.
(at around 4 mins) After Superman saves the cosmonaut and brings him back to the space capsule, he tells him in Russian, "You'll be safer singing in here." How could he have known the cosmonaut was singing? He didn't show up until after the shuttle was struck by the satellite and the cosmonaut was floating away, by which point he had definitely stopped singing.
Not only would Lacy not only have suffocated almost instantly , she would most definitely have burned to a crisp as soon as she and Superman reentered the atmoshpere .
(at around 20 mins) Lex Luthor is able to cut through the piece of Superman's hair holding the heavy weight with a regular pair of bolt cutters, even though his hair should be totally indestructible (like him). Lex's cutters have no Kryptonite blades, which would enable him to cut the normally indestructible hair.
(at around 59 mins) Superman has vision power to rebuild the Wall of China, though he's never had a power like this in any other films or incarnations. (this power was decided in post-production, due to the film's money problems).
(at around 39 mins) When Lex Luthor pretends to be a 5 star general, the insignia on his cap and shoulders of his jacket show 5 stars in a straight line when in fact it should be 5 stars that form the shape of a pentagon.
(at around 1h 20 mins) After Superman pushes the moon in front of the sun to weaken Nuclear Man, the latter's hair and cape are moving in a manner that suggests air blowing through them, despite the fact he is supposed to be in the vacuum of space.
(at around 1h) Nuclear Man descends into a volcano. While there may have been heat from lava for him to feed off, he would have no sunlight to reach the interior of the mountain.