In the Ft. Bragg scene dated 1980, portraits of both President Reagan and Defense Secretary Weinberger can be seen hanging on the wall; although elected in 1980, Reagan was not sworn in until 1981 and soon thereafter appointed Weinberger.
When the naked Norm Pendlleton is shooting at his fellow soldiers on the courtyard at Ft. Bragg, after each shot a shell casing can distinctively be heard dropping on the tarmac; during the last shot however, Norm is standing on a grass patch, where the falling casing should not be making such a sound.
The scene in which Clooney's character (Lyn) is on top of the car the morning they wake up in the desert, it can clearly be seen that Lyn leaves a large dent in the car. In the next scene the dent is gone.
When Bob awakens in the desert, and runs from the car looking for Lyn, footsteps in the sand show at least one previous take. In the preceding scene, as Bob scans the same area (prior to running from the car), the sand is shown to be pristine, without footprints.
As they are captured by Todd Nixon (Robert Patrick) and his militiamen, Bob Wilton (Ewan McGregor) raises his arms to surrender and his t-shirt rises up exposing his belly button and midriff. 2 scenes later, and still wearing the same clothes as they escape from the ambush, the t-shirt is much longer as it reaches way past his waistline - it's clearly a different shirt.
In the scene where Lyn Cassady hits the rock with the car you can see Bob Wilton is not wearing his seat belt right before the accident. However as the impact occurs and the camera pans to Bob you can the seat belt holding him in place.
After escaping captivity, Lyn and Bob chase down Mahmud in the pickup truck. In the shots from inside the truck, Mahmud is running in the middle of the road, only veering off at the last moment, while all other shots show him running on the side of the road.
In the desert "cooking dinner" scene, the placement of the silver/blue cooler is mismatched between shots. In shots facing Lyn, the cooler is within grabbing/reaching distance of him. In shots facing Bob, the cooler is 6 steps away from Lyn, near the car (Lyn is shown taking 6 steps to and from the cooler in subsequent shots).
You cannot get a dishonorable discharge from an investigation board. Only a general court-martial can give a DD. Furthermore, DDs can only be given to enlisted personnel. Commissioned officers are given a dismissal from the service, which carries the same penalties and social stigma associated with a dishonorable discharge.
In the opening scene BG Hopgood is supposedly at Ft. Bragg, the home of the 82nd Airborne Division. The unit patch on his left sleeve indicates that he is a part of the 2nd Infantry Division, primarily based out of Ft. Lewis, WA and South Korea.
In the LSD scene at the end of the film, troops are seen driving an armored personnel carrier around. The vehicle is a FV432 which is a British Army vehicle and has never been used by the American army.
At one point the New Earth Army is asked to help find General Manuel Noriega and their supposed psychic answers: "Find Angela Lansbury". In fact, at no point was Noriega in hiding. He briefly sought refuge in the Vatican Embassy after the invasion of Panama, but US forces knew he was there.
When Bob and Lyn are driving near the beginning of the film, they pass a sign that says "Baghdad" in English and has the Arabic spelling underneath. The Arabic is written left to right in the film, when the Arabic language actually reads right to left.