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)
Continuity mistake: When Kevin goes to the grocery, he buys Tide detergent. While walking home, the two bags break, but no Tide detergent falls out.
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: The movie starts in 1985, jumps '5 years later' and then back to Sasha Luss, then '3 years earlier'. So, in her crusty apartment in an impoverished neighbourhood of 1987 Soviet Russia, Anna is filling a form on her notebook-style laptop, too modern for the era. It looks like a NEC UltraLite (considered the first notebook style laptop) which didn't even come out until 1989, let alone the likelihood of someone in the USSR having one.
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.
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: It is barely credible that a young Victorian woman like Elena would even think about wearing a goatskin miniskirt - exposing her legs in those days would be akin to walking about topless nowadays. Even if she did those bright yellow cotton knickers - gleefully visible in the scene in the beehive - are in no way from the 1860s. Her pants are a hundred years ahead of their time.
Visible crew/equipment: When Lionel returns to the jazz bar and discovers Billy Rose has been killed (framed as a suicide), you can see two people standing in the shadows to the left of Lionel as he enters the main room where the stage is located. A man is hunched over, whilst a woman is standing still wearing what looks like a dust mask. (01:32:27)
Plot hole: Any strike on a military facility by incoming aircraft would first take out the SAM sites with missiles to clear the way for said aircraft to operate freely. After all, the Tomahawks fly right past the attacking planes and take out the runway with no issues at all - no reason they couldn't hit the high and exposed SAMs.
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: In circling over Washington Dulles, a plane would fly over several airports that they could land at with perfect communication, including Richmond, Baltimore, Andrews AFB, etc. Also, there is no communication from the airport to the plane but the plane would be in range of no fewer than 15 transmitting stations that could have relayed messages.
Continuity mistake: Right before they rob the police car, a Boeing 747 (four engines) is seen in shots of the plane coming into land. When the plane is shown from behind, it is a Boeing 767, with only two engines and fewer main landing gears. (00:30:10)
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 spear gun and dangling on the line behind it. Suddenly adding about 200kgs 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)