Factual error: An An-12, the aircraft the main character uses to fly all over the world, has a maximum range of about 3,500 miles. Hardly enough to fly from the US to South Korea or from South Korea to Israel. The An-12 also miraculously transforms into a C-130 in a couple of filler scenes. And why is this ex-Soviet aircraft marked in USAF markings, assigned to McGuire AFB?
Factual error: The coastal wall in Sydney is shown as being inside the Sydney Harbour (right next to the Opera House). But Sydney Harbour is not on the Pacific coast but a part of the Parramatta river, several kilometres from the ocean (where the wall should have been). So the wall is either not shielding the northern part of Australia or (more likely) the producers decided that the audience cannot tell that it is Sydney unless we see the Opera House.
Factual error: When the Iron Patriot armor is shot at on Air Force One, the bullets ricochet and smash a window. The windows on Air Force One are bulletproof. (01:32:55)
Factual error: After the USS Vengeance blasts the USS Enterprise out of Warp, Sulu says that they are 237,000km away from Earth, but the Moon is between both ships and Earth. Earth's Moon is about 380,000km away from our planet, so the Moon should have been way behind the combatants.
Factual error: When the shuttles are approaching the station, their engines are firing from the rear, meaning they are in constant acceleration toward the station. When arriving at a station, you would need to slow down as you approach, meaning the engines should be firing forward (or the shuttle should reverse direction). This happens in all scenes where shuttles are approaching the station.
Suggested correction: But the station spins to create artificial gravity for the outer rim where the ships are headed. The ships approaching are just matching speed and don't need to fully brake.
Not when accelerating toward the structure. They would have to slow their approach, then match the radial velocity of the ring, which would still mean decelerating to match the structure's relative position in orbit.
Factual error: In the Shinkansen fighting scene, the railway line is seen having color light signals along its way. But the Shinkansen uses a signalling system that doesn't involve the use of light signals at all.
Factual error: In the beginning scene, Roadblock melts through the fence using some high tech gloves. The design and application of these gloves make no sense realistically. For one, the gloves are open fingered, thus causing great risk to Roadblock of even just a melted metal drip with a slight breeze. The intense heat, even if directed down towards the fence metal, would still be enough, if able to melt through metal in an instant, to burn his fingers as well, even from behind. It would be much safer, much easier, and much more practical to have the same type of device as an external stick or long object, or even an extension of a gun, keeping the hands out of harm's way. (00:01:50)
Factual error: Superman begins shooting his super intense heat vision at the soldiers attacking him and the other heroes. His vision cuts boats in half, and incinerates the soldiers into ash in an instant. The lasers from his eyes are super strength, with him not yet knowing how to hold any of it back or shut it off, and it is going through the soldiers and boats. Yet the vision leaves no damage at all to the ground the soldiers were standing on, nor does it create any steam when going across the water cutting boats in half. (00:52:15)
Factual error: They inject the infected Brunel with antibiotics to fight the bacteria, however there is no pulse and that means the antibiotic can never spread through the body, as there is no blood circulation.
Factual error: When Jack retreats to the cabin for the first time in the film, he puts a Led Zeppelin record - Led Zeppelin II - and plays the first song on that side of the record, which turns out to be 'Ramble On'. Any Zeppelin fan would know that 'Ramble On' is song number 7 on side B, therefore the needle should have been placed somewhere in the middle of the disc. The first song on that side of the album would be Heartbreaker. (00:33:55)
Suggested correction: Not "any Zeppelin fan" would know this, only those that know the song order on this album.
This isn't a valid correction. You're just nitpicking at the wording of what a Zeppelin fan would know.
Factual error: In the final scenes when Superman is fighting the enemies in Metropolis, even though half the city has been destroyed, the lights are still on in many buildings. In reality, the destruction of a few skyscrapers would be enough to trigger the shutdown of the electric substations that serve the city and all the lights would be off (as happened with Hurricane Sandy). (02:00:00)
Factual error: In this relatively low-budget but extremely well-produced 2013 science fiction film, a 6-man crew travels from Earth to Europa (one of the moons of Jupiter) to search for traces of life in the vast oceans beneath Europa's icy surface. One of the astronauts dies in-transit, leaving 5 crewmembers to complete the mission. When the large "Europa One" interplanetary spacecraft arrives at its destination, all 5 surviving crewmembers descend in a small landing craft to the moon's surface, leaving the Europa One spacecraft in orbit, totally unmanned. This is an inconceivable factual blunder. The narration plainly states that this mission picked up where manned lunar missions of the 1970s left off; so, many of the same protocols are in place. Just so, no manned space mission would ever abandon the primary space vehicle in orbit, placing the mission at risk by sending the entire crew down together in a landing party. At least two astronauts should have remained aboard the orbiting Europa One just in case the landing mission went sideways (as it does in this film).
Factual error: In "China", when the white American guy shoots the flying monkey out of the air you can see the slide on his pistol locks back. However, he is then able to fire a second shot a few seconds later. (00:32:03)
Factual error: Admiral Hadley often barks orders ordering Army forces to act, not just Navy forces. He wouldn't have the authority.
Suggested correction: Can't speak to the second half of your paragraph (should really post as 3 separate mistakes) but as for the first, a range of 3500 miles, aircraft such as the kc-135 exist and aerial refueling is fairly common place. Considering it's a mission supported by the acting UN Secretary General to stop a world crisis, resources could have been diverted for refueling.
The initial launch from the carrier is a C-130 which can do this (if empty, minimal fuel, has the full length of the flight deck and the carrier is steaming full ahead into the wind). It then morphs into an AN-12 and back to a Hercules. They make the point that this small fleet is what is known to remain of allied forces so not sure where any tanker support will come from. Many movies have ridiculous range issues with aircraft anyway.