Plot hole: The fact that a five minute timer starts after the three Cerberus codes are entered defeats the purpose of the program. If they program was made to destroy their own nuke warheads in case of a misfire you would expect them to be destroyed as soon as all three codes are in. (01:38:20)
Other mistake: When Casey is in the car boot on the phone to Jordan, Jordan is asking her to describe what she sees in the boot of the car. Casey is naming the items she sees, paint cans, shovel etc. Jordan asks her to pour the paint out of the boot through the tail light hole. Jordan puts out a call to look out for a car with "WHITE paint pouring out the back," but Casey didn't tell her the colour of the paint.
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.
Continuity mistake: During the chase scene on the bridge involving the tank, two cars (silver Toyota Corolla hatchback, licence NE34 12 and a black VW Bora, licence NU67 67) appear during many shots, often travelling in different directions on the bridge and either ahead or behind the chase.
Revealing mistake: When Han shoots at Bruce Willis and the others with the Gatling gun, we see cartridges on the ground. You can tell that they are all blanks. The tip is jagged and has been closed - live ammo just has an open hole where the bullet was.
Revealing mistake: When Nica crawls to the elevator to escape Chucky, she bends her legs in order to shut the elevator door. She is meant to be a paraplegic and have no feeling in her legs.
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.
Character mistake: When Harley asks Tony what the light is coming from his chest, Tony responds "an electromagnet." Harley replies "What does it power?" An electromagnet is not a source of power. The arc reactor is the power source which powers both the electromagnet (to keep Tony safe from the shrapnel near his heart) and the Iron Man suit. (00:43:25)
Plot hole: Each of the four magicians are given a tarot card that has a date (March 29), a time (4:44pm), an address (45 East Evan St), and a city (NY). When they enter the building on that date, they know which apartment to go to. The problem with this is that it was never stated on any of the cards which apartment to go to once they reached 45 East Evan Street. (00:08:40 - 00:10:05)
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."
Other mistake: The old man executed in District 11 was shot in the head from behind. However, when Katniss looks out the window from above there are no blood stains on the floor, nor is there a gunshot wound to the head. (00:20:50 - 00:22:30)
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: 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)
Plot hole: The most secure prison in the world, designed with the advanced schematics of world leading prison-building architect (J.D Ray Breslin) has cameras somehow interconnected to one another so tightly that physically neutralizing one puts every other camera out of commission as well.
Continuity mistake: In the scene when Yuri's daughter is getting away from the hotel, the color of the chopper changes from green to brown between shots.
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.
Audio problem: In the scene where the polite leader is addressing the Sandins for the first time he takes his mask off and starts talking to the camera but he is muted until James unmutes him. If you watch the polite leader while he is muted he mouths the words "Mr. And Mrs. Sandin" before he is unmuted. However when he is unmuted we hear him finish that statement by saying "Mrs. Sandin" again. (00:33:25)