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.
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.
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.
Factual error: Major Marco's uniform in early shots has a Special Forces tab on the left breast pocket. This doesn't appear later. Also, this tab should only appear on the dress blues, where shoulder insignia are not worn.
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.
Deliberate mistake: When Denzel Washington is in the bathroom, he discovers the camera monitoring him from the air vent, by seeing the light on the front of the camera. Any spy with common sense would not install a hidden camera with a light on it.
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.
Revealing mistake: Sen. Jordan is supposed to be an expert kayaker, but when paddling his kayak it is very obvious from the way he splashes the tips in the water that he cannot paddle.
Character mistake: When Marco is trying to raise his rifle to assassinate Senator Arthur, he held it upside down with his scope below and turned over in the same scene, He is an expert marksman.
Chosen answer: Perhaps the piece-of-plastic killing was a "test run" by the brainwashers to see if Raymond would actually react to their commands. You can see other soldiers lying down wearing "halos", hinting that this happened at a different time and place than the observation room choking.