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.
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)
Revealing mistake: When Anna and Hans are dancing in front of the lighthouse, we don't see the shadow of the railing or the ground they're standing on.
Continuity mistake: In the scene where the witch gives Mika the dagger to kill herself with, the witch stabs it into the floor. When the witch leaves the dagger is lying on the floor. When Mika goes to grab the dagger it is stuck in the floor again. (01:15:20)
Continuity mistake: When Viper confronts Shingen, she removes her left glove twice.
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.
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.
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.
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.
Continuity mistake: When Tom the Minion dressed as a maid is hoovering, he answers the front door by opening it towards him as does the minion who looks out of the door after Tom has been taken. In the scene with Gru sat on the steps in the rain, sad that Lucy is off to Australia, Agnes comes out with an umbrella, but now the door opens outwards.
Continuity mistake: In the scene where grandpa is attempting to ship his grandson to his dad in a cardboard box, grandpa says to the two ladies who are objecting to his requests "well give me a pen, and we'll write FRAGILE on it." Shortly before he says that, the box already says "FRAGILE" on the right hand side, and then 2 seconds later the writing has disappeared. (00:31:10 - 00:32:15)
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)
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.