Factual error: Atropine is on two occasions in the movie stated to offer some kind of protection against corrosive gasses. First, against the nerve agent/gas Goodspeed encounters in the beginning of the movie, which is corrosive enough to eat through a protective suit. Secondly, near the end of the movie against the cloud of VX gas; here Goodspeed injects Atropine into his heart and survives without a scratch even though it is stated that VX will melt your skin. While Atropine is used to counter the effect of nerve agents, Atropine (or any other drug invented by man) wouldn't do anything against a gas that can eat through a protective suit or dissolve skin. In this case the muscle contractions created by the nerve agent would be the least of your worries.
Factual error: When Cage gets into the Ferrari, the camera changes for a few seconds showing the gearbox. In slow motion it is obvious that Cage shifts into 3rd gear instead of 1st, however the car makes a very impressive tyre-burning start. The F355 is indeed a very powerful car, but this would be simply impossible to do in 3rd gear.
Factual error: In the scene where Frye and Darrow confront Hummel after he sent the rocket off-course, Major Baxter barks at Darrow: "You're talking to a general, soldier. Maintain discipline." We've been told that all the men are Marines, and that even though they are committing treason, they view themselves as Marines. No Marine, particularly a career officer, would address another Marine as "soldier."
Factual error: When the Seals team swim towards the rock they are aided by microsubs, which all have headlights that are on. The light would be reflected at the surface and would be detected in the blackness that is all around. They do not need lights, all they need is modern technology to direct the subs, which they have. Details like this would have been determined during the planning of this operation, and fully trained Navy SEALS would know better either way.
Factual error: When the pilots are being briefed about the mission to bomb Alcatraz, they are in the front of the hangar, and an F/A-18 is between them and the camera. There is an AIM-9 missile on the left wingtip of the jet, but no dome cover. AIM-9s always have a protective cover over the seeker head of the missile to keep the eye from drooping when power is off the jet.
Factual error: During the car chase scene the cable car used was not from the California line (despite the signage on the trolley saying it was) as it had open seats and a driver area at only one end. This type of trolley is used on the Powell Mason line where there are turntables at the end of the line. California line has open seats and driving levers at both ends, so it can change direction without a turntable.