Factual error: At one point in the movie the sun is behind the helicopter and we can see that the places for the missiles are empty. However, he's shooting right after that.
Factual error: At the end, when Cyndi Lauper touches the glowing pyramid, goes into a trance, and starts translating the inscription, Jeff Goldblum pulls her off and she doesn't finish it. One of the bad guys says that what Cyndi already said will be enough to help him decode the rest and that it's just a matter of "cartography" now. He should have said "cryptography" (skill of decoding secret writings) and not "cartography" (which has to do with making maps).
Factual error: When Jack is trying to buy the bus tickets, the bus company employee tells him that his credit card was cancelled. Credit card companies do not divulge that type of information, they simply indicate whether the requested charge is accepted or denied.
Factual error: Group Captain Massey is referred to several times, even by British officers, as "Captain" Massey. Group captains are always called group captains.
Factual error: Near the end when MacPhearson tries to hide away from Dave Ryder in a large room, two men are running up a stairway one behind the other. MacPhearson shoots the one in front, which unrealistically, causes no reaction in the other man, who is directly running behind him, so MacPhearson can shoot him easily too.
Factual error: Shooting at a gas tank with buck shot at 50 meters distance will not make it explode (it likely won't even dent the surface), and lead pellets do not cause sparks when they hit.
Factual error: The sequence showing the moon is incorrect as it shows the Moon as it looks from the northern hemisphere. It should be inverted.