(at around 1h 35 mins) Luthor says that Krypton exploded in 1948, and that it took three years for the rocket that carried Kal-el to reach the earth, so it arrived in 1951, and he should be around 3 years old. Yet when Clark is in high school, it still appears to be the 1950s judging by the fashions, cars, and songs played on the radio.
(at around 1h 16 mins) When Superman first grabs the wing of Air Force One, his "S" is backwards, revealing a flipped shot.
(at around 58 mins) At the train station, the New Haven engine that masks Otis's entrance to Luthor's lair and the one that hits the detective Harry are the same unit, number board 5048.
(at around 2h 10 mins) Superman pulls Lois out of her car and lays her on the ground with her arms pointing down and her clothes are all dirty. Yet when he screams in rage and takes off, her right arm is up by her head and her clothes are clean.
(at around 53 mins) When Clark and Lois are leaving the Daily Planet on Clark's first day, he tries to follow Lois into the revolving door, getting his briefcase stuck. So, he then goes into the partition behind Lois. But when they come out into the street on the other side, they exit from the same partition. They enter the door separately but exit together.
(at around 1h 45 mins) A "500 Megaton" bomb would do far more than cause California to have massive damage. The largest nuclear weapon ever detonated was only 57 MT and caused damage up to 170 miles away. 500 MT would be more than twice the power of the eruption of Krakatoa, the largest explosion in recorded history.
(at around 1h 6 mins) No heliport would ever had electrical cables strewn across the helipad as shown on top of the Daily Planet building.
The missiles fired were shown to be BALLISTIC and not cruise missiles. They would rise to a high arc into the lower atmosphere and then descend upon their targets. They wouldn't have flown parallel to the terrain until they reached their targets.
Actual footage of two Minuteman I ICBM's test launch from Vandenberg AFB was used in movie. Minuteman is not capable of non-ballistic, low-altitude, cruise flight as seen in movie.
(at around 1 min) In the opening sequence, when the film dissolves to show the Daily Planet building, the camera tilts up to show the Moon, but the view shown is one that is not visible from the Earth, as it shows a large amount of the Moon's far side.
Superman is fast enough to fly around the world seemingly faster than the speed of light to reverse time yet was unable to stop both missiles. Even Superman had to deal with air resistance in the atmosphere, whereas in space, there was none.
(at around 1h 23 mins) When Superman meets with Lois for his first interview, she already knows and explicitly asks about powers he had demonstrated during the previous night's rescues, specifically his invulnerability and X-ray vision. A robber on a getaway boat struck him with a crowbar the night before, and he X-rayed her lungs to check for lung cancer just one minute before they sat down to begin their interview.
(at around 1h 45 mins) When Clark jumps out of the Daily Planet window on hearing Luthor's ultrasound tone, and changes into his Superman costume instantaneously on the way down, his legs stay clad in Clark Kent's trousers. Obviously it was not an instantaneous process.
(at around 21 mins) The recorded teachings by Jor-El in baby Superman's capsule states there are 28 known galaxies. By the 1960s, the Catalogue of Galaxies already listed 29,418 galaxies. Kryptonian understanding of galaxies may have been different.
(at around 1h 16 mins) After Air Force one is struck by lightning and her crew apparently panics, the Captain instructs one of the others to inform the ground that the president is aboard. While "Air Force One" only becomes so when the President is aboard and the notification would not be needed, it was a life and death situation and the crew did not care about protocol at that moment.
(at around 1h 12 mins) When Superman is catching the cat burglar falling down the side of the skyscraper, his cape (also note the burglar's flashlight) is flat against his body revealing the tilt camera special effect.
(at around 32 mins) When they do the pan shot of the town site just before the cemetery scene, on the grain elevators, the logo for the "Alberta Wheat Pool" is clearly visible on the green grain elevator.
(at around 2h 10 mins) When Lex Luthor and Otis are brought to prison at the end of the film, the flaps of Luthor's bald cap are clearly visible on the back of his neck (especially when he tells Otis to shut up).
(at around 2h 5 mins) After the Hoover Dam breaks sending a wall of water towards the homes, there is a scene where a telephone pole by a dock is springing back and forth by the force of the water - an obvious model.
(at around 1h 55 mins) As Superman is reaching out to grab the missile to hurl it into space, you can see the scaffolding used for Christopher Reeve to lie on sticking out inside his suit (moulded to fit his chest and tummy).
(at around 56 mins) When plainclothes Detectives Harry and Armus are tailing Otis through Grand Central Station, Armus leaves Harry saying he's going to call for backup, when a uniformed officer literally is standing just a few feet behind him.
(at around 16 mins) Jor-El wears an alien device with an uncanny resemblance to a Rolex watch on his wrist.
(at around 36 mins) The Cheerios box in Martha Kent's kitchen is a 1970s design, when this scene must be set in the 60s.
(at around 1h 15 mins) The little girl who is audibly slapped by her mother after getting her cat returned by Superman, clearly isn't, judging by her shadow on the wall of her house.
(at around 52 mins) Director Richard Donner is reflected in the Daily Planet revolving door when Clark and Lois are leaving (just after the "swell" exchange).
(at around 21 mins) When the planet Krypton explodes, you can clearly see folds in the cloth on the ceiling that makes up the black "space" surrounding the planet. Explosions that are supposed to take place in space are photographed from directly underneath so the sparks "fly" evenly in direction of the camera.
(at around 2h) When the gas station explodes, as Lois escapes in her car, we can clearly see a camera sitting on the back seat.
(at around 28 mins) After jumping across in front of the moving train, a reflection of the cameraman can be seen in the train windows as Clark runs home.
(at around 1h 7 mins) During the sequence of Superman's first rescue, police and fire engines are shown responding to crash scene. Shooting briefly from inside the fire truck, the camera drives past a row of four or five location crew campers.
(at around 2h 5 mins) Hoover Dam sits at the head of a long, narrow canyon, which ultimately leads into Lake Mohave, and does not have any towns downstream within sight of it.
(at around 1h 45 mins) Although Metropolis is represented exclusively by New York City throughout the film, in the shot where the passengers in the bus see Superman fly by outside and one says "That's Superman!," the background plate of the building they're passing that's used in the effects shot from inside the bus is actually a shot of Robinson's department store on 7th Street in downtown Los Angeles.
Superman told Miss Tessmacher he would get the missile headed towards Hackensack first. It has always been assumed that Metropolis is NYC, or at least a "twin city". While it isn't known from where exactly the missiles were launched, there is no way that Superman would have had to chase the first one through a desert. In fact, he likely would have been able to intercept the first on the way to the second, costing him no time at all getting to the California missile.
(at around 44 mins) When Jor-El introduces himself in the Fortress of Solitude, he explains that by this time, he will have been dead for thousands of Earth years. Yet during his teaching during Kal's journey to Earth from Krypton (at around 21 mins), Jor-El refers to Einstein's theory of relativity, which wasn't formulated until long after the destruction of Krypton.
The day after Lois has her interview with Superman, there is an extensive article in the newspaper. The article includes a picture of Superman. Lois didn't take any pictures, and since he was unknown before that, there wouldn't be a picture for her to include unless she took one. No explanation is given for how she got the photo.
(at around 30 mins) [expanded version] The little girl on the train that watches Clark Kent run fast, appears to be young Lois Lane, when Clark arrives in Metropolis only 12 years later, Lois is a full-grown woman (appearing to be at least 25 years old). The young Lois should have been a teen.
With the amount of damage sustained to the car that Lex flips over, no one in the army convoy makes mention of the fact that Teschmacher has not one scratch or injury on her body.
When Superman goes back in time, everybody seems to remember events that have yet to happen (like Lois and her car and Jimmy and the Hoover Dam). The only person to remember would be Superman himself.
(at around 1h 40 mins) When the commentator on the TV is reporting on the missile launch, he says that he is at the launch site, at ground zero. However "ground zero" would refer to where the missile is due to land, not where it's launched from.
(at around 1h 16 mins) The pilot of Air Force One describes their position as "Ten miles - that's Ten-er miles" from the airport. The scriptwriters have incorrectly extended the aviation custom of pronouncing the number "nine" as "niner" to avoid possible confusion with the German word "nein", which means "no". The -r ending isn't added to any numbers not ending in 9. In addition, for distances of more than one digit, the digits are pronounced individually: "One-Zero Miles", not "Ten Miles".
(at around 1h 50 mins) Although Kryptonite weakens Superman, there is no significant reason as to why he cannot remove the chain itself and throw it away like Ms. Teschmacher does.
(at around 1h 4 mins) When Clark turns and goes down the hall from the ladies room, the extra passing him looks right the film crew.
(at around 30 mins) Young Clark says he can make a "touchdown" every time he kicks a football. Kicking a football through goalposts is a field goal, not a touchdown.