Revealing mistake: In the beginning, there is a scene where Sen. Shaw is watching Raymond make a speech on a TV screen. It was obviously put in in post-production because the aide immediately next to the screen is nodding and clapping in agreement at inappropiate times.
Factual error: When Eleanor Shaw tries to convince other members of the senate to choose her son as a candidate for vice president, a map of the fifty states and their corresponding electoral votes can be seen. The map shows Colorado as having 3 electoral votes and Wyoming having 8. Wyoming should have 3 and Colorado 9.
Revealing mistake: When Raymond Shaw's skull is being drilled to implant the chip, bone "dust" comes out. This never happens, since always some blood comes out and the bone debris are mixed with blood and therefore unable to "fly" like wood or plaster debris.
Audio problem: Near the end of the movie the helicopter is flying into the area where the troops were held. The radio traffic isn't pilots or air traffic controllers, it's railroad dispatchers and trackside detectors.
Factual error: One of the Gulf War scenes shows Marco and Shaw's armored vehicles in the Kuwaiti desert with a skyline of burning oil wells in the background. We later hear that this sequence is set during a reconnaissance in Iraqi-controlled territory just before Desert Storm. Saddam's troops only set fire to oil fields during the end of Desert Storm as they were retreating from Kuwait.
Continuity mistake: When Marco is in the library searching the internet for information about the scientist, he isn't wearing headphones. Then he notices the security camera recording him, and in the next shot, from the camera's POV, he's wearing them. When it cuts back to 'our' regular view they're gone again immediately, and he puts them on to listen to the computer.
Continuity mistake: In the scene when Liev Schrieber is with his mother before they go out to the party, she kisses him, than starts to lean forward to kiss him again. But when the camera cuts to the reverse angle, she hasn't moved an inch. It's as if she lunges back to her original position.