
Continuity mistake: The green Alfa in the opening minutes has its side, and mirror, wiped out by a lorry. For the next 5 minutes it then drives around in perfect condition. (00:05:43)

Factual error: The vents that Hunt and his sidekick crawl down at CIA Headquarters are standard galvanized steel box vents; they are very common in the building trade. Try walking or crawling down one - you'll make a noise like the sky is falling down. People will be able to hear you for miles. Every person in that building would know somebody crawling about in the vent system. (This error applies to dozens of films, not only this one).

Factual error: Amongst the essential parts of a nuclear weapon's detonation mechanism is a radioactive isotope of tritium, which has a half life of just 12 1/2 years. The tritium in every nuke on earth has to be replaced every ten years or so. This is by no means unusual; there are other perishable parts including detonators made of conventional explosives which would be completely inert after a thousand years. After lying dormant with no maintenance at all for that amount of time the nuclear weapons the 'Man-animals' find would be big shiny paperweights and not much else.

Continuity mistake: When Portnow meets with Bishop at the church, in the first closeup of Bishop's crossword puzzle the word "MUD" is the second word across at the top, and at the center of the puzzle the 4-letter word "GEAR" is written in the 5-letter answer - with the fist space left empty. However, in the next closeup of the puzzle, now the word "ETA" is the second word at the top and "MUD" is the third, and the word "GEARS" has the "S" added, with the letter "G" started properly in the first space of the answer. (00:10:15)

Factual error: The radar guided SAMs are consistently evaded/triggered by the pilots' flares, which in reality only work against heat seeking missiles. Radar guided missiles would be defended against using chaff, basically clouds of aluminium foil strips. It was mentioned in some interviews they didn't want use chaff as it wouldn't really be visible for the audience - hence why they only deploy flares.

Factual error: Near the end of the film, Knox is flying a Huey helicopter, and the Angels hitch a ride by shooting it with a speargun and dangling on the line behind it. Suddenly adding about 200kg to a Huey in flight like that is going to cause all sorts of problems with the trim and airspeed of the aircraft. The pilot would know immediately that something was wrong. (01:23:20)

Continuity mistake: When Pierce's wife is walking in her auto shop they pan down to show her red Louboutin heels, then they cut to her walking in her office, and when they show her shoes again they have a tan sole.

Visible crew/equipment: After Indy and Henry have escaped from Castle Brunwald, Indy jumps into one of the boats, pulls the motor starter cord and jumps back out, then just as he bends over to release the boat from the piling, right between Indy's legs the black covered arm of a hidden crew member appears from under the tarp taking hold of the throttle, steering the boat away from the pier. (01:02:40)

Visible crew/equipment: When Tom and Sonic pull over and the mini drone explodes, knocking Sonic unconscious, the camera pans away and you can see emergency vehicles blocking the road on the right of the screen, presumably closing down the road for filming. (00:59:55)

Other mistake: Murphy lands the helicopter on a railway line so an oncoming train will destroy it completely, and this happens exactly on cue with huge, dramatic explosions and flying debris. Apparently the train driver doesn't think this is important enough to interrupt his busy schedule - he doesn't stop the train. We do not hear brakes being applied - the wheels would make a noise like the sky coming down - and the train doesn't slow down at all - it just keeps on going.

Other mistake: When the stormtroopers break into the control room, the stormtrooper on the right of the screen hits his head on the door frame. On the DVD release they've added a thump when he hits it. (01:18:55)

Visible crew/equipment: On the train, Jack hears Mac saying the track isn't finished, then Jack becomes aware of the broken emergency stop button. When Jack walks back over to Annie and tells her they have to jump, we can see the reflection of the standing camera operator on the right door's window, and the reflection of a crouching crew member (possibly boom operator) on the left door's window. Definitely crew given they're meant to be alone on the train. (01:45:55)

Continuity mistake: When Sam is in his bedroom, after he finds the Cube sliver it falls and dramatically burns a hole through the floor into the kitchen. But Sam's bedroom is over the living room (there is nothing on the ground floor below Sam's elevated bathroom, and in the first movie Jazz hides in this open space), and the kitchen is actually located between the den and dining room, at the other end of the house. If they were to follow the actual floor plan of the house, the Cube sliver would have landed in the area of the piano in the living room, but where would the fun have been in that? (00:12:30)

Factual error: During the war games they have Jefferson pose as a major in order to facilitate the commandeering of the ambulance and the jeep. Regardless of their personal feelings in the matter the ambulance crew and the driver and troops in the jeep would be perfectly aware that no black man would ever be promoted to a position of authority in an otherwise all white command. We may find it repugnant today but the US Army was rigidly segregated during World War 2 - and it stayed that way until 1948. Jefferson may have been inducted into a special unit like the Dirty Dozen but considering that the future of the entire mission is riding on their success at the games, throwing it all away like that makes no sense at all.

Factual error: Why is Hilts not wearing a uniform? A serving officer captured behind enemy lines in civilian clothing risked being shot as a spy. If a prisoner's uniform was too worn or damaged to wear, it was routine for the German authorities to replace it - a P.O.W. in civilian clothes is an obvious escape risk. He is wearing a pair of tan chinos, a cut off sloppy Joe sweatshirt, both ridiculously anachronistic - Sixties hipster fashions - and nowhere even close to a World War 2 uniform. He is also wearing Army Type III Service boots - something that would never have been issued to a fighter pilot.
Suggested correction: Hilts was a POW for a few years before being transferred to this camp. His current clothing likely changed from when he was originally captured in his uniform, so he would not have been considered a spy. After multiple escape attempts, his uniform could have been ruined. The Geneva Convention required that POWs receive shelter, food, clothing, medical care, etc. The Red Cross delivered care packages to POW camps containing food, miscellaneous apparel, and other essentials. Sweatshirts have existed since the 1920s and changed little. Also, chino pants have been around since the late 19th century. Hilts was an U.S. Air Force pilot, and light-colored khaki trousers (similar to chinos) were standard-issue uniform for some U.S. military branches, along with leather bomber jackets for Air Force pilots. Therefore, he is dressed appropriately for his military branch.
And none of them would have been available to a prisoner in a German POW camp in the mid 1940s. Not one single item of hipster fashion would have found its way into the camp. Even if it did, do you really think the German authorities would allow a prisoner to lounge about in civilian clothing? Talk about an escape risk.
The camp was in Germany, not Poland. Other than the sweatshirt, Hilts appears to wear military clothing - a leather bomber's jacket with military sleeve insignia, and U.S. Air Force khaki trousers. So not "hipster" '60s civilian clothing. The sweatshirt could be military appropriate (even issued) and something Hilts acquired at a different camp. He arrived with a small duffel bag that presumably had some misc clothing. He and two other POWs are the only Americans and have different uniforms. The current camp commandant, who apparently disdained Hitler and his Nazi minions, would decide what POWs could wear.

Audio problem: When Luke says, "Now all we gotta do is find this Yoda, if he even exists," if you look closely, his mouth never moves.

Visible crew/equipment: After Willie spits in Indy's face it cuts to Short Round running through the mine, and just as Shorty turns his head toward the camera behind him, we can catch a glimpse of something blue which does not belong in this dark dreary environment, at the right side of the screen. There is a tall spotlight and two crew members, one is wearing a solid blue shirt and a cap, and the other a blue/white striped shirt with white pants. (01:21:25)
Suggested correction: This takes place in milliseconds and there's no way to see it unless you pause the image or play it in slo-mo. It should be under trivia.
Right now I have it playing on Netflix, and there is no slow motion. The striped blue shirt is noticeable as it plays without any slo-mo. If something catches my eye onscreen, it is fair game to go back and rewatch what was noticed in the first place. And in order for me to confirm what I find, I do pause, and may take screenshots. By the way, I've seen this movie countless times over the years, and it was just a matter of catching that glimpse of the color blue because it popped out against the dreary surroundings. I'll leave it up to Jon whether to move it to trivia or not.

Visible crew/equipment: In the "Battle of Carthage" in the Colosseum, one of the chariots is turned over. Once the dust settles you can see a gas cylinder in the back of the chariot. (01:22:55)

Continuity mistake: In the final fight scene on the plane between Jinx and Agent Frost, Jinx is slashed across her stomach, drawing blood. In a later scene, when Jinx and 007 are pouring diamonds over one another in the hut on the cliff, her stomach is unblemished. (02:02:25)

Factual error: It is impossible for a stream of burning jet fuel to follow a plane through snow and catch up. Not only is jet fuel extremely hard to ignite, almost as soon as the plane was off the ground the fuel stream would be too dispersed for the flame to climb up into the tank, and even if not it wouldn't burn fast enough to catch the plane.
Suggested correction: Knox wasn't a trained pilot. Either he had no clue to what was going on, or he thought something may have been wrong, but didn't know what to do about it.
Taking off and landing a helicopter are by far the most intense and difficult part of a pilot's training. Seriously, 99% of learning to fly is learning how to land and take off. If the pilot is skilled enough to take off in a Huey he is easily skilled enough to notice a massive additional drag on his helicopter due to the additional weight of the angels and the air resistance put up by such a bulky protrusion on his aircraft. If he isn't skilled enough to notice that, he isn't skilled enough to take off in the first place.