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 first time Brad Pitt leaves the aircraft carrier he is on an Antonov An-12. I haven't been able to find any evidence of an Antonov An-12 being able to take off or land on an aircraft carrier. The minimum runway distance for takeoff is 1500 m, and A Nimitz class carrier is only 325 m. (01:22:00)
Suggested correction: Most planes, if not all, that don't have vertical takeoff capabilities can't land or take off on aircraft carriers. That's why systems are in place to launch planes up to speed for take off and to catch or stop planes upon landing. Even jets that are 5 times faster than a An-12 need help with take off and landing.
A C-130 did multiple take-offs and landings aboard a carrier WITHOUT any assistance, so yes, an AN-12 might have been able to do the same thing: https://theaviationgeekclub.com/the-story-of-how-the-c-130-hercules-became-the-biggest-aircraft-to-land-on-an-aircraft-carrier/.
Factual error: When we are at the Welsh WHO facility we get an exterior shot during the night where we hear crickets chirping. This is a classic US film-making error. There are no crickets in Wales or any part of the UK. What you would hear at night is silence. Maybe owls.
Suggested correction: What on earth makes you think there are no crickets in the UK? The most common type found in the UK is the field cricket (Gryllus campestris). In total there are over 25 types of crickets in the UK. Ture that some species are mute, but not the field cricket.https://en.wikipedia.org/wiki/Gryllus_campestris.
Crickets in Wales don't make a noise as they do in warmer climates.
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.