Continuity mistake: At the beginning Ava shoots the man's phone out of his hand through the car window. When the car drives away all the windows are intact.
Visible crew/equipment: When Henry helps pull Mark onto the treehouse at the beginning of the film, if you look very closely to the left you can just make out a crew member dressed in black helping him on to the platform. The crew member then ducks back under the platform.
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.
Visible crew/equipment: There is a shot of Holly crawling through a tight space with the camera facing her moving backwards as she crawls forwards (about 30 minutes into the film). In this shot, the wheel marks of the camera can be seen on the ground in front of her. (00:30:05)
Factual error: Jack Ryan takes the enlisted oath, not the officer's oath, when commissioned into the Marines. (00:02:35)
Plot hole: Bond makes a huge tactical error after diving to the St. Georges. He knows the Russians and their operatives are after the ATAC. The ATAC itself is expendable to Britain, since it has a self-destruct mechanism that, under proper procedure, would have been set off when the ship sank. So why is Bond trying to retrieve it? Because he disarms the self-destruct, he actually allows Kristatos to get his hands on it, forcing Bond to track it down again and, to stop the Russians from getting it, HE DESTROYS IT! So why doesn't Bond, instead of disarming the self-destruct, set a timed charge or toss a grenade in the room to destroy the ATAC while it's at the bottom of the sea? The answer is, of course, that if Bond destroys the ATAC before the bad guys can get at it, the movie's over. Even so, at the end, when Bond finally does destroy the ATAC, he tells Gogol it's "detente. You don't have it. I don't have it." Clever line, but it reinforces the fact that the British don't need it. They can build another one.
Factual error: It's mentioned that the British and New Zealanders turned the Americans away. This is untrue - the Americans stayed with both for a time until it was decided that they would be safer with the Canadians.
Factual error: When the house explodes, there is a massive explosion and fireball that creates a pressure wave strong enough to send Brian flying into the van. However, not a single window breaks on the houses just feet from the explosion. (00:15:40)
Visible crew/equipment: When Freddy falls over the banister onto the stairs near the end, notice the crash mat he lands on. (01:18:55)
Factual error: The Pentagon is the largest office building in the world. It has seven floors, 28 kilometers of corridors and 620,000 square metres of office floor space. The idea that the entire building could be searched in one afternoon by six people is beyond absurd. If those six people could search an average of one office every five minutes and they worked twenty four hours a day, seven days a week they'd get through the whole building in 89 days and 15 hours. I don't think the punter they are looking for has a lot to worry about.
Factual error: In the big battle scene at the Home Mart store after Robert turns the power off to the building, you see Robert grabbing welding canisters. When Robert has Ralphie turn the power back on, it cuts to one of the bad guys in the break-room, and a digital microwave starts counting down. A digital microwave could not have any memory of any prior cook settings, let alone any way to set it, since the power was already out. (01:55:40 - 01:56:35)
Continuity mistake: In the scene where Ruby and brother are driven to Terry's crash site the police cruiser changes from a 98 model to a 97 model. The vehicles headlights, front bumper and over all design are completely different.
Continuity mistake: In a scene towards the end of the movie, where Bond and Vesper are lying on the beach, Bond has sand on his back throughout most of the scene. When they start to kiss, in the distant shot towards the end of the scene, he has no sand on his back at all. (01:57:10)
Continuity mistake: In the scene at the bar with Gideon when the black guy pours Gideon a drink it is only about 1/3 full. When Gideon drinks it in the next shot it is almost full.
Visible crew/equipment: You can see the string that pulls Bubba off the bike when Max shoots him. (01:19:41)
Continuity mistake: When Sonic and Tails are fighting metal Robotnik, he shoots glue at Tail's tail. Tails says he can't fly to help Sonic, but when he gets the piece of concrete to surf across the water on you can see that his tails are not glued together.
Factual error: The terrorist with the AK47 is unaware of the fact that a Harrier is hovering just outside the window until he slowly turns and see it there. He does a double take when he sees the Harrier just five metres away! A Harrier is an incredibly loud aircraft; you can hear them from three kilometers away. At that range the floor would shake with the noise and he would have been in no doubt whatever that he had been under attack for some time.
Continuity mistake: Nick Cage is chasing Mason in the yellow Ferrari. The windshield breaks at least twice, but is perfect in the next shot. (00:45:55)
Revealing mistake: In the shooting scene in the Mount Rushmore cafe, a boy in the background puts his fingers in his ears, because he knows the gun is about to be shot.
Factual error: When they go into the water, they put mouthpieces in, but, a few times, they talk to each other, which is impossible with mouthpieces in.
Suggested correction: Sorry to burst your bubble here but there is scuba equipment which allows for talking whilst using a regulator.
They're not wearing such equipment. In the movie they're just wearing regular mouthpieces.
In the DVD commentary the writers explain that the divers should have been wearing full face masks which allow for communication, but the director changed it for mouthpieces, but kept the talking in. They pointed out this mistake.