During Operation Market Garden, the US Airborne troops are shown being driven in trucks. However the US Airborne troops had no vehicles assigned to their outfits and therefore walked/marched off their landing zones in Holland, 1944.
At the end of the film, SSG Vogel is depicted as wearing a Combat Infantryman Badge (CIB), with a star on it. The star denotes a second award, meaning he would have had to have fought in the 1991 Gulf War (the criteria for the CIB does not award a second CIB for serving in both Iraq and Afghanistan), something he is far too young to have done.
Vogel's in the 82nd Airborne Division, but in the flashback to Market Garden, he's wearing regular infantry fatigues and not a paratrooper suit like the rest of the guys in his outfit.
In one scene, SSG Vogel says, "Let's go check on the lieutenant colonel." In the U.S. Army, lieutenant colonels are referred to and addressed as "colonel".
In the Market Garden flashback, the German officer asks Vogel if he has a family using the familiar grammatical form (which is used with family, friends, and children) and not the formal, which is used with strangers.
When Staff Sergeant Vogel and the other soldiers are being flown out of the war zone in a C-130 transport, we hear almost no background noise. However, the C-130 is very loud (many passengers even choose to wear earplugs while flying in one).
In the end credits, Captain Larson's rank is incorrectly shown as COL (colonel).
There is no way young Kyle at the size he was shown could have carried the loaded footlocker by himself. WW2 era footlockers empty would weigh about 30 pounds (approx. 13.5 kilos). Adding all the items in there would have made it at least 50-60 pounds (approx. 23-27 kilos).
The Soldiers in the film are shown wearing a newer version of the Army Combat Uniform (ACU) that was not yet available in 2005. The IR tabs on their shoulders are always shown to be folded under the pocket, but the original ACU had the IR tab itself on the outside of the pocket and had to be covered when not being used.
In the Market Garden flashback of October 1944 one of the American troopers is wearing an American flag patch on his arm. The American flag patches were worn by most 82nd Airborne troopers on 6 June 1944 and discarded within a day or two. They weren't worn again after that.