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)
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.
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.
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 Ryan enters the space station and removes her spacesuit, she is shown wearing only a tank top and boy shorts. In reality, according to NASA's official webpage, astronauts wear a liquid cooling and ventilation garment and an absorption garment (space diapers) under their suit. (00:38:45)
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.
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: When Fin stops near the school bus, the bus number changes from "278146" to "278245" during the rescue of the kids.
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: 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: 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.
Continuity mistake: In the lifeboat on the way to the mainland, Capt Phillips sometimes is clean-shaven and sometimes has stubble.
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: 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.