Revealing mistake: When Tommy Ross gets killed and Carrie looks at his supposedly lifeless body if you look closely you will notice he blinks revealing that he is actually alive.
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: 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: 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: 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.
Character mistake: In the scene where Nicki is being interviewed by Vanity Fair, she refers to her younger sister, "Gabby." Nicki is the character based upon Alexis Neiers. In the movie, her younger sister's name is supposed to be Emily. Gabby is the real life name of Alexis' younger sister.
Character mistake: When Katie's husband arrives in town and confronts her on the night of July 4th, he says "I miss you Katie." He does not know her name to be Katie as that is the name she created when she came to town. He is married to Erin.
Suggested correction: He says "I miss you, baby" and then "I miss you so much, baby."
Continuity mistake: When Teresa is yelling and hitting Jordan because he cheated on her with the blonde girl in the limo, the car disappears and reappears between shots. (01:00:35)
Continuity mistake: During the dinner scene at Tom's, a couple of shots before Tom's phone rings and he goes to answer it, Nick's wine glass is about half full. After Daisy leaves to go to Tom and the shot cuts back to Nick, the level of wine in his glass has notably decreased, without him touching it. (00:09:50)
Plot hole: They aren't able to travel before the birth of their children or their children become different. Despite that, he visits his father one last time before their third child is born. His Dad and he then travel back to when he was a kid, which would have changed his first 2 kids.
Suggested correction: This is not necessarily inconsistent with the movie's time travel logic. Since Tim goes back in time to visit his father and inside that particular time travel, they use time travel to go back to a day where Tim was a child. Then, they return back to the original time travel where they're playing ping pong. At that moment, both of Tim's kids were already born. So, when he returns from the ping pong scene, there's no change regarding his kids.
Also, paraphrasing the Dad, he said they aren't going to change anything. It is more like reliving a memory than changing the future to get what you want. The Dad couldn't go back to not smoke before his kids were born because that was major and would have changed the course of his life; walking a bit differently on a secluded beach that you walked on in your younger days (as long as you spent the same amount of time - presumably) would not alter the trajectory of one's life.
The slightest change in 1 second of being on the beach would absolutely affect his kids. A man produces 1500 new sperm every minute. Altering the timeline and delaying every event that is going to happen by literally 1 second would most definitely alter which exact sperm was used when conceiving both of his first two children.
Continuity mistake: When Theodore goes to Amy for comfort in her apartment, there's someone (or something), walking at the front door, but then not again in the next shot. Keep your eyes top right, it's very visible. (01:26:50)
Visible crew/equipment: When the young lady is trying to drag her dead husband away to bury him, as she takes a hold of the blanket you can see the covered wagon in the background and someone's legs behind the wheel begin to move to the right. She was suppose to be alone except for her dead husband. (00:34:00)
Continuity mistake: When Walter Mitty is on the skateboard riding towards the Icelandic town, there is a shot of him riding along wearing Nike Frees, the camera then cuts to a close up of his shoes and the board, and the shoes in that shot have changed to Vans authentic.
Continuity mistake: In the shot where Holly is done injecting Anna with the syringe and stands up to shoot at Detective Loki, the syringe and two "medicine/poison" bottles are all close together next to Anna's hair. Next three shots showing the room far out with Holly getting shot and killed has the two bottles next to the edge of the rug and very far from Anna's hair, as well as the syringe which is slightly closer, but far away. The next shot of Loki picking up Anna has the syringe and bottles in their original position next to Anna's hair.
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.
Revealing mistake: Early on, after Clary blasts the demon with a homemade explosion that blows a huge fireball across the kitchen and blasts out the window, there is no sign of anything being burned, not even the curtains. The kitchen is only in a slight shambles and there are small fires burning in isolated areas that never spread or char anything.
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)