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: 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: 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 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: 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: 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: 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 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: 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: 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.
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: In the final scene where Solomon was reunited with his family, the doors he entered the room through had Edwardian style leadlight glass. The movie was set about 50 years before this style.
Factual error: When the seals are tumbling down the mountain one of them almost lands on a rattlesnake. There are no rattlesnakes native to Afghanistan or any other part of Asia. They occur only in the western hemisphere.
Factual error: As Wendell and Jackie are driving in the car, Jackie turns the radio on to put a hiatus on their discussion. As soon as he turns it on, sound issues forth, but in the 40's radios used vacuum tubes, which required a warm-up period.
Suggested correction: Once the tubes are warmed up, they will tend to stay warm for a period of time even if the radio is turned off. It's possible the radio had been turned on and warmed up before this scene.
Factual error: When Bradley Cooper calls Louis C.K. he asks him, "Where are you?" Given he's just called him on his office number, rather than a carphone, he knows exactly where he is.
Factual error: When Jordan tries to escape with his daughter in the Mercedes, he pulls the parking brake with his hand (a hand-type parking brake) to stop the car, but that car (Mercedes Benz SL Class R129) is only available with a foot-type parking brake, making his action impossible. (02:43:35)
Factual error: In the scene where the young Helen Goff is traveling by train with her family, it's obvious that an American engine and coaches have been used, instead of a Queensland Rail locomotive of the era. None of the QR locomotives had flared smokestacks like on the one seen in the movie. The coaches are also incorrect - as far as I know, none of the Queensland Rail wood coaches had clerestory roofs with a set of windows in them like seen in the movie. When Helen looks out the back of the train, it's also obvious that the tracks are spaced at 'standard gauge' (4' 8.5"). They should be closer together, as railways in Queensland are built to 3'6" gauge instead. There is also no such company as the 'Queensland Victoria Railway Co', as marked on the coaches, as all railways in Australia are state owned.
Factual error: A scene near the beginning of the movie when Forest Whitaker and Oprah are both speaking on different phones. The phone that Forest is using has a modular plug. The scene takes place during the Kennedy administration (early 60's). The modular phone plug was not patented and put into use until 1975.