In the opening Gulf War scene when SFC Shaw is telling the men inside the transport that they will be moving out soon, one of the men presses the stop button on a stereo CD player to stop the music playing. The music stops, but it can be clearly seen that the CD was never spinning in the first place.
When Marco removes the implant from his shoulder, he accidentally drops it into the sink, considering it lost forever. However all he has to do to retrieve it is to screw open the odor trap underneath the sink, since it has not been flushed away yet. A soldier should have that basic technical knowledge.
In the election war room, when Shaw's mother is rallying to get her son on the ballot, she stands in front of an electoral map that lists Wyoming as having 8 electoral votes and Colorado with 3. These numbers, if written by a "political expert" would be switched.
When Major Marco is in the library investigating the Manchurian Global corporation's doings, as the camera finds him, it shows that he's wearing headphones in the camera's recordings but after that we see that he's actually not wearing them and he's shown putting them on a couple seconds after to listen to the doctor on the computer.
When seeing the red star on the stage through the scope the carpet is already littered with confetti. In the previous shot there is at most one unexplainable piece of confetti to the left, and while there are cut-aways before the scope shot, it is immediately after this that the confetti starts to fall.
In Rosie's cousin's apartment, Bennett Marco sticks his finger through the grating on the vent in the bathroom. From one side, we see him put his finger in the second hole up. From the other side of the vent, his finger goes through the fourth hole up.
In the last scene of the movie you hear radio chatter over the aerial beach shot. The audio says "NS 10 milepost 79.81, No defects." While this may sound like military radio traffic, what this actually is is an automated announcement system for a railroad safety system. A track side detector for Norfolk Southern Railroad (i.e. "NS") located at milepost 79.81 has just had a train pass by and no axle bearings were overheating (i.e. No defects). This is the message that the train engineer hears over his VHF locomotive radio after the train passes the detector. This was not appropriate radio traffic for this scene.
Apparently, FBI surveillance cameras come complete with big red record lights, and FBI undercover agents are not wired remotely. Instead they carry dictaphones, mark up the tapes clearly with the target's name, then keep them in their handbags, which they leave lying around while they sleep.
In the opening scene where the "Lost Patrol" is ambushed, Captain Marco is shown driving the truck while Sergeant Shaw is riding in the passenger seat. This is highly unusual in Army doctrine, as the senior most ranking individual will ride as the vehicle commander, sitting in the passenger seat. This is also true as an Officer, generally, will not engage targets on the mounted machine gun.
In the early scene of Major Marco talking to scouts about his war record, he is asked if he was wounded, and he says that he was, but a close look at his chest shows no Purple Heart among his ribbons. If he was wounded in action, he would have a Purple Heart. He is, however, wearing a Silver Star, which is exceeded only by Distinguished Service Medals from the several military departments and homeland security; service cross medals for Coast Guard, Navy, Air Force, and Army; and the Medal of Honor.
The goof items below may give away important plot points.
In some shots the blood stain on Raymond Shaw's shirt is on his chest, but in the last shot (where Raymond and Eleanor are lying, back to the ground, on the floor and the camera is panning out upwards) the stain is much lower, around his belly.
The civilian guide in Kuwait is listed in the credits as "Laurent Tokar," but both the newscast that announces Shaw's nomination and the newscast describing Tokar's arrest at the end of the film call him "Laurence Tokar."
When Marco shoots Shaw and his mother, at the time Marco pulls the trigger he is aiming near the top of Shaw's back. The bullet should enter Shaw's back high up and then pass through him lower down into his mother's body. When they are shown lying dead Shaw is wounded in his stomach and his mother is wounded high on her chest.
On the surveillance video showing Marco being stopped by security on Election Day, the date shown is 17 November. The latest a general election can be held is 8 November, as they are held on the Tuesday after the first Monday in November.
When Major Marco learns that Rosie is not who she claims, he opens a file that has his college information on a letter head from The Citadel. Closer inspection of the ring he wears is not a Citadel ring. His ring has a stone in it where Citadel rings are solid gold with the palmetto, state seal, and class year.
During the candidate's victory speech, Marco's rifle is poked through the grill/grate in the balcony. At the angle shown for the gun, the scope's view would have been obstructed by the grill/grate. However when he is shown looking through the scope, he has a "clear" unobstructed view.