Revealing mistake: When the kids are burying Gus, his supposedly dead face flinches when they shovel dirt on him.
Continuity mistake: When Fox and Wesley first jump off the building onto the moving train, Fox has on boots with heels, but when she lands on the top of the train, her boots are flats.
Revealing mistake: Before Paxton is hit with the 3 prong instrument, you can see the bloody holes already on his shirt. (01:01:20)
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.
Continuity mistake: The case files which Agent Cowles brought to the kitchen and put on the countertop disappear shortly after being placed there. (00:08:30 - 00:09:10)
Revealing mistake: When the new Pope is announced, the New York Times headline is shown, and 'Copyright 1990 The New York Times' is visible. The event took place in 1979.
Revealing mistake: On the ice the tank is firing - in slow motion we see empty shells are littering the area. The shells have crimped ends, revealing them to be blanks.
Factual error: The movie takes place during the 1990s, but throughout the movie cars are shown with Illinois license plates with "Illinois" written in cursive. These plates were not introduced until 2001. (00:24:45)
Continuity mistake: When surrounded by police and a garbage truck, Frank drives his car from the overpass onto the passing transport trailer below, then lands behind a hatchback and in front of two cars - a white compact with a sunroof and a grey hatchback. In one specific shot from atop the trailer, as Frank rolls his window down (before he requests the gun) the only vehicle behind Frank's car is the white compact, which is at the trailer's rear. Note things such as the trailer's safety bars, and the view through the compact's windshield for starters. That grey hatchback is back when the ramp is lowered, for the ensuing crashes. (00:08:20)
Revealing mistake: When the UFO makes the huge flash that knocks everyone in the cemetery down, one of the police officers kicks a tombstone as he falls and it wobbles back and forth. (00:13:35)
Plot hole: Inmediately after Jamie Foxx finds the bomb in the city hall, and he says, "We don't tell the mayor anything", we see Gerard Butler arriving to his property next to the prison, and finally he enters his jail cell. So, in the time between Gerard Butler's arrival to the property and his entrance to the jail cell, Jamie Foxx thought about a plan, picked up the bomb, passed through the traffic and security checkpoints, talked to the warden to get access to the prison, entered solitary, handcuffed the bomb, and still had time to wait for Gerard Butler's arrival.
Continuity mistake: When Eliot Ness is at Jim Malone's house for the first time, Malone's collar is opened, then buttoned, then open again.
Revealing mistake: When Sonny is punching Carlo under the spraying fire hydrant, he misses an audible punch by at least six inches. (01:43:30)
Continuity mistake: Towards the end, Denzel drives his car into 2 cars trying to get Ethan off the hood. After that scene ends you see Denzel driving the same car and the front and rear of the car look nothing like they did when he was crashing into the cars.
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.
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.
Continuity mistake: When Magneto lands the Golden Gate Bridge on the island, as it hits land it is still very light. When the Brotherhood start to walk toward the island, it cuts to a wide shot of them still walking on the bridge, and it's suddenly dark.
Factual error: After the intruders flood the panic room with propane, Jody Foster's character gets a lighter and ignites the propane causing it to burn along the ceiling. This would be impossible as propane is heavier than air and would sink to the floor rather than rise up to the ceiling. Lighting a flame in that room should have caused anyone in the room and on the floor to be engulfed in flames almost instantly.
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 performing CPR on Elena, Robert doesn't tilt her head back. As a former firefighter, he would know one of the first steps of CPR is to tilt the victim's head back to clear the airway. His rhythm is also way off.
Suggested correction: Tilting the head back to clear the airway isn't practised any more, due to exacerbating possible neck/spinal injuries. Instead, one would do a chin lift to clear the airway. But alas, he didn't do that either.
Paramedic here. The head tilt-chin lift is absolutely still practised today and is definitely our go to manoeuvre for CPR. You're thinking of the jaw thrust manoeuvre where we do it when we suspect spinal injury, which Elena did not have.
Former Volunteer First Responder and Ambulance driver part-time but also volunteer here. It actually depends on the SOP of the company in which you serve. Liability purpose has us practising caution in otherwise duty-to-act scenarios. While you are always to remain either Red Cross or American Heart certified in CPR, ALS guidelines and SOPs still govern the practice in which you are performing and can be effected by the decisions of your local Medical Director, but I digress.
Continuity mistake: In one of the last scenes, Cate Blanchett is standing in the doorway of her son's room. She is wearing a blue striped dress. When she walks into the room, she's wearing a floral dress.