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: Toward the end, Russell goes to talk to William at his house. He turns the chair around to sit on it backwards, and throws the shirt down onto the ground. When he sits down the shirt is back on the chair.
Character mistake: When Melanie and Scarlett are talking with an (off-screen) wounded Confederate soldier, the soldier says he hasn't heard from his brother since Bull Run. Only Northerners refer to that battle as Bull Run; Southerners have always referred to it as Manassas.
Factual error: It is not possible that Pitt could have gone up to the ship when it was already blasting off. There was literally fire in the tunnel.
Suggested correction: It was a bit confusing, but what I saw was a shower of sparks or hot particles and some fumes, and no fire in the tunnel until he was through the hatch. The makers may have been influenced by seeing vapour prior to a rocket launch, and then some rockets use a shower of electric sparks to ignite the engines. It was implausible, but no fire in the tunnel.
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 old percussion double barrel shotgun is firing modern shotgun shells, which would never work or fit in that gun, and furthermore are also made of plastic, wrong for the era.
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.
Visible crew/equipment: Near the end, when Rodmilla and her daughters are requested to appear before King Francis, in the first shot facing the king and queen, there is a beige narrow mat in front of the large patterned rug, which is not in previous or following shots, specifically used for crew/camera tracking (fullscreen version). (01:50:30)
Visible crew/equipment: While Barnum and Phillip sing "The Other Side" Phillip uses two stools to get up and down from the bar top. When he steps down from the bar top, in this wideshot (also the first shot of them in the pub and other shots) the two upright stools Phillip used are secured with additional support, note the floor area underneath the stools' legs have the same pattern as the rest of the floor, though we can see the outline where the pattern's lines don't match up. Additionally, we also see three actors' marks (in the shape of an "L") on the floor in front of the bar, which will be where Barnum and Phillip will stand when they agree on the ten percent. (00:36:05)
Other mistake: One visual that has always bothered me that I could not find in your list were the scenes when the mother ship first appears. It's enormous scale appears to dwarf Devil's Tower and the whole surrounding area actually, but when it moves over to the "landing strip" area and begins to rotate 180° (right-side up?), it suddenly seems to shrink to a much smaller size and mass during the slow revolution. On its originally-seen scale above/behind the tower, one would think that either the great ship's outer prongs would have been torn off, or more likely the impromptu landing site and most of Devil's Tower would have been destroyed as the huge craft rotated itself. The visual scales just do not stay consistent throughout the film's climactic final act.
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)
Audio problem: When Reynolds is salting the asparagus the camera cuts back to Alma and you can see Reynolds' hand moving in a different direction but the salt shaker sound is still playing. The camera cuts back to Reynolds, and he's holding the salt shaker again. (01:06:15 - 01:06:39)
Revealing mistake: When Claude and Ray are at the retirement home getting ready for bed, as Ray lifts up his shirt you will see where it looks like he's wearing a fat suit underneath. He can also be seen pulling it down to his waist.
Factual error: At the point where Jared Leto is released from prison he is picked up in a 1960 Black Chrysler Imperial. As the camera rises it shows the date as 1954. The car is used a few more times in the movie.
Factual error: When the B-52 is flying low over Russia, the shadow on the ground is a Boeing B-17G, a World War II propeller driven bomber.
Continuity mistake: When the police are moving in to arrest Dzhokhar Tsarnaev, the shot shows an FBI SWAT officer grabbing him. But in the next cut, the officer changes to a Boston Police Officer while changing back to a FBI Officer in the following shot.
Continuity mistake: The morning after Vivian's first night at the hotel, room service brings breakfast. When she's eating a croissant it cuts to a shot of Edward, and when it cuts back to Vivian she's eating a pancake which goes from being half done, to being a whole pancake again. (00:30:55)
Other mistake: The first time the cops come to the house, Connie and her son see them from the upstairs window, and start walking downstairs. It then cuts to the cops in the living room looking around, and Connie walks in and introduces herself. Her husband is not home, so did the cops just walk into in the house without knocking?
Suggested correction: I'm pretty sure the housekeeper let them in if you listen carefully.
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)