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.
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?
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.
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: 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 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: 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)
Factual error: The coastal wall in Sydney is shown as being inside the Sydney Harbour (right next to the Opera House). But Sydney Harbour is not on the Pacific coast but a part of the Parramatta river, several kilometres from the ocean (where the wall should have been). So the wall is either not shielding the northern part of Australia or (more likely) the producers decided that the audience cannot tell that it is Sydney unless we see the Opera House.
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: 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.
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: After Batman shoots Reverse Flash through the head, Flash rushes over to Batman and catches him before he falls over from his wounds. As Flash is lying him down slowly, there is no blood on Batman's face. It then cuts to a close up as Batman reaches up to pull off his mask and there is suddenly blood on his lips and chin. (01:12:20)
Continuity mistake: Approximately two scenes after Kitai leaves the pigs' burrow where he sheltered for the night, the "cutlass" is suddenly missing from his backpack. He later retrieves another from the ship's tail section. There is likely a deleted scene which would have explained the loss of the cutlass.
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.
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.
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.