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?
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)
Continuity mistake: When Fin stops near the school bus, the bus number changes from "278146" to "278245" during the rescue of the kids.
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)
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)
Other mistake: Sam draws an orange vest for Lockwood using a dark crayon. (01:10:45)
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.
Factual error: After the USS Vengeance blasts the USS Enterprise out of Warp, Sulu says that they are 237,000km away from Earth, but the Moon is between both ships and Earth. Earth's Moon is about 380,000km away from our planet, so the Moon should have been way behind the combatants.
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)
Continuity mistake: A few minutes after Lee puts a bandage on Hugh's forehead, it disappears completely in one shot (as does the cut it was covering), before reappearing a moment later, but in a different position.
Plot hole: Even if someone would make all nuclear powers launch their nuclear missiles and then destroy them you still wouldn't have a nuclear weapons free world as most of those nations have plenty of nuclear weapons in reserve. A lot would be even be armed and ready to go for a possible second strike. (01:24:10)
Continuity mistake: Towards the beginning of the movie, Gerry's son spills hot coffee all over Gerry's shirt. He is wearing a white shirt/vest for his uniform. There is no stain or even wetness left behind.
Plot hole: According to the flight recording, Odyssey was on an uncontrolled pull towards the Tet as Jack says, "We're not getting away from this thing." So even if Jack jettisoned the sleep module where Julia was in, the module should not be able to get away as the whole ship is being pulled towards the Tet.
Suggested correction: It can be assumed that the jettisoned module has enough "jettison power" to force it away from the command pod. And in turn that force would move the pod further towards the Tet. It's reasonable to assume the Tet couldn't pull the module that was moving away, under dramatic force, and to which it didn't have line of sight (which was blocked by the pod).
Other mistake: The driver for the general at the end of the movie is referred to as captain, but is in the credits as Major Carrie Farris. (02:09:50 - 02:15:35)
Character mistake: In Pitch Black they established the system they crashed in (M-344/G) had 3 stars. Jack stated it when the 2nd sunrise started, and the solar system model also had 3 stars. In this film when Boss Johns starts asking about M-344/G he says it is "a backwater system with 2 suns and 1 habitable planet."
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.