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: 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: 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: Lauda is an Austrian. Yet when his name appears on scoreboards with his country abbreviation, it shows AUS, which is for Australia. AUT is for Austria.
Factual error: In the office motel of the Dallas Buyer's Club, a calendar behind Ron Woodroof's desk shows a newer model of a Lamborghini Aventador (2011-current) but the story takes place in 1985.
Factual error: In the final fight scene with Malekith, Thor falls through a portal that brings him to Charing Cross station, where the lady on the train tells him he has to ride 3 stops to get to Greenwich. Charing Cross is not on the Jubilee Line and so not directly connected to Greenwich - even then it's a lot more than 3 stops. (01:33:45)
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: 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: A number of press photographers are present during the trial of the Great Train Robbers and they take a series of photographs of the opening proceedings. No photographer has ever been allowed in a British courtroom for any reason at any time, ever.
Factual error: The movie takes place in the early 1850's, referencing the rumor of gold in California. The girl, while rummaging through the wagon, comes across a pair of boots with zippers up the sides, zippers that wouldn't be invented for another 50 years.
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: 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: 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 train liveries shown in the UK were well out of use by 1980. And the West Coast Railway (Company) did not exist at all.