Factual error: When Sandra Bullock and George Clooney manage to get to the ISS, she gets entangled with some ropes and manages to grab Clooney's safety rope. Clooney's speed should be very close to Bullocks' and the ISS', hence. The parachute ropes should be able to withhold the forces of deceleration (the mass of two people is very small, compared to Soyus or ISS), so no more pulling or having to sacrifice himself... This is due to the fact that there's no drag in space to constantly change Clooney's velocity (revert to Newton's First Law).
Suggested correction: The parachute ropes are of course strong enough to hold the relatively low kinetic energy of the drifting astronauts, but that is not the reason why Clooney detaches. The rope is not attached firmly to Bullocks' leg. There are some loops loosely wrapped around her leg, and while both astronauts are still drifting away from the ISS (seen in a shot a few seconds earlier), those loops slip away from the foot one by one. Before the last loop slips away from the foot, untethering and condemning both astronauts, Clooney detaches himself to lessen the kinetec energy that pulls on the rope by reducing the total mass of the "system of two astronauts", so that there is a better chance that the last loop will remain attached to Bullock.
Once Clooney had stop moving all that would have been need was a slight pull from Bullock to pull him towards her. The momentum was lost when he stopped moving. So no need to cut himself loose.
It all happens in free fall. As soon as the cord withstood inertia resulting from George's body mass pulling on it, George would bounce back towards Sandra. The entire scene was completely unrealistic.
Clooney stopped moving in relation to Bullock. But both were still moving in relation to the ISS (look at the scene again; there is a wide shot that establishes this), with both their masses pulling on the parachute cords, straining the tenuous connection of the cords looped around Bullock's foot. To lessen the strain, Clooney detaches itself from the two-astronaut-system, reducing the mass and kinetic energy pulling on the cords.
Clooney and Bullock - when they were connected to each other - never actually stopped moving in relation to the ISS.
Actually parachute cords can withstand hundreds of pounds of force, making them very difficult to snap.
The danger wasn't the ropes snapping, the danger was that they would slip off her foot, and they would both be lost to space.
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?
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.
Factual error: Near the finale, Kang sends a command to all US based missiles to self-destruct in their silos, thereby detonating their warheads. Ignoring for the moment why "self-destruct in silo" would ever be a desirable scenario programmed into ICBM protocols, detonation of a nuclear warhead requires an extremely precise sequence of events, none of which would include a nearby, conventional explosion. (01:38:20)
Factual error: When Sawyer and Cale take Cadillac One ("The Beast"), they eventually want to shoot a rocket launcher at the fence. Sawyer wants to do this while hanging out of the window. The real Cadillac One is bullet proof and has several layers of glass with the final one softer not only to prevent the bullets entering but the deadlier threat of glass pieces. Only the driver side can open approximately 3 inches.
Factual error: The movie is set around 1995. But the SWAT team in the movie is wearing gear from the 2000s. (MICH-2000 helmet, modular tactical vest, M4 variant with picatinny rails and scope). Plus, in a scene when the guys are shopping for a taser (gun shop scene), some of the rifles on display are from 2000s era. AR-15 variants with variant stock, foregrip and picatinny rail. Those style of weapon system were unheard of in early 90s. Even Special Forces just adopted it by the late 90s.
Factual error: In the scene where the Navy Seals are riding in the cars, the VA state vehicle inspection can be read from behind. It read "6 13" for June 2013. This would have been correct for the period the film was made, but not for the time of the incident.
Factual error: In the scene where Shaw is talking to a goon while fixing his car he states the simplest things cause the most problems while holding a spark plug. We know this can't be right as Brian concludes the car is a turbo diesel like a Le Mans car, which would actually use a glow plug and not a spark plug. (00:19:50)
Suggested correction: That's exactly the problem that Shaw is referring to, a member of his team installed the incorrect plug which caused a problem, i.e. a Spark Plug and not a Glow Plug (a simple thing, causing the problem), along with the 'good' being simple minded and causing the rest of Shaw's team a problem.
The glow plug isn't what causes combustion in a diesel like how a sparkplug does for gas. The wiring harness for a spark plug vs a glow plug is completely different and they aren't interchangeable. You can't just accidentally put a spark plug in a diesel, it doesn't work like that.
Factual error: The Whyte character says it is Checkmate even though he moved the queen into a position that doesn't threaten the king and could not have blocked anything that does threaten the king. You can also see all positions that might threaten the king, and none of them do. (00:27:40)
Factual error: In the beginning of the movie, Leah Templeton is killed on Feb 26. Then the newspaper obituary that Jordan had hanging on her locker door says that Leah's service was to be held at 11am on Feb 27. That is not enough time to prepare the body and get her ready for her funeral by 11am the next morning, especially since it's a murder under investigation.
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: 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: It is not plausible that the tail rotor blade of the helicopter can destroy large parts of a building without being damaged. (01:24:40)
Factual error: The dude handcuffed to the radiator has a single piece of duct tape across his mouth maybe 8 inches in length. The sweat and oils, and somebody just moving their mouth will break the tape free from their mouth. A person can scream all they want. To properly do it properly, a ball gag like the one used in Pulp Fiction needs to be used. A piece of tape does nothing, I've taped my own mouth to try it. (00:46:30 - 00:47:30)
Factual error: When they are in Costco there is music playing in the store. Costco does not play music in their stores.
Factual error: The moving truck that transports the Perron family's belongings didn't exist in 1971. It is a 1973 model or newer.
Factual error: Halcombe takes a left turn to park in the parking lot of the Army/Navy Surplus store on 4th Avenue. This means he was approaching from C Street, which is a one way street in the opposite direction between 4th and 5th Avenue. (00:15:00)
Factual error: The sign outside Einsargen Prison says "high security area." For some inexplicable reason, the German writing just above reads "Hochsicherheitssteckdose", thus declaring the area to be a high security electric wall outlet. (00:25:40)
Factual error: At the fair, one of the guys sets some hay on fire and the fire goes to a cage of propane tanks. They begin to explode. The explosions are way too small for full propane tanks. You can tell they are supposed to be full as several shots show the red caps on the valves are faintly visible. The red caps are kept on ones that are full and unused. (00:12:40)
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.