Revealing mistake: When Mason is having his hair cut, after finishing up, he is talking to Womack and turns his back on him. If you look at the back of Mason's neck, it is clear that he's not just been freshly shorn; there are whorls of hair just above his collar. (Either that, or the barber was terrible at his job).
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. (00:44:14)