(at around 1h 40 mins) Although Vera Webster presses a button which is marked INVISIBLE SHIELD, Superman is then enveloped in a visible shield.
(at around 1h 12 mins) When the Olympian carrying the torch that Supes blows out goes up the stairs in the wide shot, the torch is a sparkler-type, sending out sparks instead of flames. In the close up of the torch going out, there are flames instead of sparks.
(at around 43 mins) When Superman returns Ricky to Lana after hitting his head on the rock in the wheat field, Lana wipes the blood off his face with her white sweater. In the next scene, the sweater is spotless.
Even if it were possible to build a supercomputer without technical specifications and instructions only on cigarette wrappers and napkins, it would have taken weeks, if not months to transport, construct, test and operate the device and not it the short time depicted.
Clues for the year the film is set in is very inconsistent. The year on Gus' cheques read 1983, the high school reunion states it's the 20th anniversary of the class of 1965 graduates (making it 1985), the Summer Olympics briefly shown should be happening in year 1984.
(at around 3 mins) The blind man's seeing-eye dog takes off after another dog causing all the trouble in the beginning. This is taking liberties for the sake of comedy as seeing-eye dogs are specifically trained to ignore other dogs in the performance of their duties.
(at around 52 mins) Gus "programs" the weather satellite to create a tornado. Weather satellites don't control the weather, they only collect data.
When Gus analyzes the Kryptonite fragment, the satellite lists the following elements: plutonium, tantalum, xenon, promethium, dialium, mercury, and an unknown element. All are elements in the periodic table, except dialium. Dialium is a genus of plants.
Gus' synthetic kryptonite is 15.08% plutonium, a usually man made element although small traces of natural occurring have been found. In either case though, this amount should be dangerous even to Gus, who is seen grabbing it at least twice with his bare hands, and the Webscoe technicians who manufactured it.
It would be impossible to steal half cents or less as the accounting would be off. All companies would be using accountants to balance to ledgers each month. Gus would have been caught after the first attempt of theft.
(at around 1h 50 mins) Superman's super strength doesn't appear to be enough to break away from the supercomputer when it's 'sucking' him in. The supercomputer knows his weakness (kryptonite), and that's what's likely being used to defeat him.
(at around 1h 11 mins) At the Olympics, people in the crowd are waving Scottish Flags. Scotland competes as part of the United Kingdom, so the Union Jack should be waved. They could be Scots cheering on a Scottish athlete.
The kryptonite Gus gives Superman brings out an evil side to him. Even though kryptonite should only weaken him (make him normal). However, it's not kryptonite from Krypton, it's kryptonite made from Gus using ingredients he found. It can have a different effect.
In one scene, Superman arrives too late to save a truck from going off the bridge and into a river. Though in the first film it shows he has the ability to circle around the world and go back in time before it happened. Since he's starting to have the effects of the tainted-kryptonite, he's becoming irresponsible and not thinking clearly.
(at around 1h 24 mins) Superman uses his heat vision to melt a mirror (that's showing his reflection). Even though the heat vision is usually like lasers and should reflect (as it did in the previous installment, Superman II (1980)). It's likely it was a different 'heat vision' type Superman can control and was using.
(at around 8 mins) Most of Gus' fantastic BASIC program is empty PRINT statements.
(at around 1h 19 mins) The hull of the oil tanker sailing to Metropolis is high above the water line, which means it's empty. If the tanker was fully loaded with crude oil, the gray paint on the hull would be below the water line.
(at around 58 mins) When Gus has skis on the roof, he wears leather shoes. When he smashes through the railing, he wears ski boots. He wears ski boots again on the angled glass ceiling, then regular leather shoes when he lands on the street.
Superman's flying wires are visible at several points, including: when Evil Superman flies into the auto junkyard, when Superman lands on top of the Statue of Liberty, at the chemical plant fire, and when Superman saves Ricky.
(at around 1h 30 mins) During the junkyard fight, Superman kicks Clark Kent, who's on his knees, in the face. Clark falls to the ground unconscious. In the next frame, shot from a distance, Superman picks Clark up in his arms and Clark noticeably grabs on to Superman's back to help himself up. At the same time, Superman visibly struggles to pick up Clark.
(at around 23 mins) At the reunion dance there is a US flag against the wall improperly displayed with the union to the right.
(at around 1h 13 mins) When Lorelei is secretly reading Immanuel Kant's 1781 philosophical work "Critique of Pure Reason" and Ross, Gus and Vera return she hides it under a pillow and picks up a magazine. As she lays back her foot accidentally bumps the pillow hiding the book and it falls off, exposing the book.
Ross Webster disappears after the cave-in happens (due to the Super Computer being destroyed) and is presumed dead, yet later Gus Gorman asks what will happen to Ross (and others). Since Gus was only there briefly after the cave-in it's likely he's unaware of Ross' fate.
The villains use a weather satellite to analyze fragments of Krypton's remains in deep space so as to manufacture Kryptonite to use against Superman. Firstly, weather satellite aren't used to look into deep space, radio telescopes are. However, no matter what machine was used, it would be impossible to pinpoint the remnants of a planet that exploded thousands of years ago in a distant galaxy.
Trained police officers would not open fire on bank robbers in the middle of a crowded city street as seen during the opening sequence as this would endanger the lives of innocent civilians..
(at around 44 mins) When Gus tries to gain access to the computer facility by showing the security guard a case full of spirits, the reflection in the door of Gus does not match what is being said.
(at around 1h 45 mins) On the subway, after the Ultimate Computer drains Metropolis's power, Ricky speaks without moving his lips.
(at around 1h 40 mins) Towards the end of the film when Superman is in the cave, he is encapsulated in an "invisible shield" bubble. The wires holding the bubble off of the ground are clearly visible in numerous shots.
(at around 19 mins) Just before Superman lands with Jimmy in his arms (at the chemical fire), you can see the shadow for the rigging that supports Superman and Jimmy and their wires on the yellow fire truck in the background.
(at around 19 mins) Before and after the firefighters put Jimmy on the stretcher, the shadow of a boom microphone is visible to the left of the headrest.
Set in America, yet the spellings of defence, colour, and unauthorised reveal that it was filmed elsewhere.
In one Smallville scene, a Canadian bank logo is clearly visible in the background.
(at around 52 mins) When Gus programs the Vulcano Satellite, he enters the coordinates of Colombia 75ºW 5ºS. Those coordinates correspond to Peru. Colombia is more like 75ºW 4ºN.
(at around 1h 15 mins) When Gus shows Ross and the others his plans for the Super Computer, all he has are a bunch of crude drawings of his computer and he only has a general idea of what he wants to do with it (defense capabilities and so forth). Even when the construction workers are assembling the computer, they only have the crude drawings to work with, yet when Ross and the others reach the computer, they instantly know exactly how the whole thing works (what buttons to push, etc.)
(at around 1h 40 mins) Superman has trouble breathing inside the "bubble" the supercomputer covers him with, but he can still fly in space. Even if there was Kryptonite-usage with it, he wouldn't be able to use his 'heat vision' to get himself out of it.
When Lana is looking at the picture of Clark from high school he isn't wearing his glasses so when Superman is in Smallville at the ceremony honoring him Lana along with anyone who saw Clark's picture in the gym and attended the ceremony should have recognized him as Clark Kent.
(at around 50 mins) It is difficult to believe that one's altered Bloomingdale's invoice would arrive in the mail on the same day that Gus is still working to hack into the Vulcan satellite and within the very few short hours he is there.
To eject two "keys" at the same time into the computer, Gus uses unconscious Brad's arm (pulling it with a yo-yo) for the other key ejection. It would've been easier to attach the key firmly to a stick to do the other at the same time. (though Gus might not be thinking the easiest way).
(at around 45 mins) When Gus is trying to get Brad drunk, and Brad complains that there is not enough vodka in his Singapore Sling, the drink he has is not a Singapore Sling. It is a translucent brown liquor which appears to be whisky or brandy; a Singapore Sling would be an opaque pink.
(at around 59 mins) After Gus has instructed the computer to look for Kryptonite, the computer returns the mis-spelled line "instructions recieved".
When the evil Superman is getting drunk in the bar, he should not have been affected by drinking the alcohol. Superman is impervious to weapons and other things that might threaten the average person, and the alcohol should have had no effect.
(at around 14 mins) Gus attempts to break into the payroll records, but misspells "override" as "overide".
(at around 1h 24 mins) After Supes is exposed to the tainted kryptonite, he stops shaving, stops bathing, stops cleaning his laundry, and starts drinking. However, when he's at the bar flicking the nuts at the bottles of booze, his fingernails are clean, cut, and nicely manicured, and his hands are also clean. This after causing an oil spill in the Atlantic.