Sergeant Major MacGregor's hair (both on his head and on his face) are completely against US Army regulations for their length and lack of grooming.
Uniform violations abound in this film. Primarily when the characters are "in garrison" and not in the combat areas or on patrol. In the staging areas you see troops in all kinds of combinations of physical fitness uniform or DBDUs (Desert Battle Dress Uniform i.e. fatigues). Hats, no hats. T-shirts only, no shirts, etc. This was not allowed except maybe within a tent or possibly in the makeshift gym. Everywhere else you'd be in full uniform, sleeves down, hat or helmet on, etc. You could also be in the PT uniform, but it had to be complete and you carried your weapon everywhere. If not, some Command Sergeant Major would scream at you. You weren't even allowed to wear your sunglasses around your neck or pushed up on your head. PVT Ocre is right when he gets yelled at for not blousing his boots. That happened all the time.
Both M-60A3 main battle tanks and AH-1 attack helicopters are shown being used by the US Army in the movie. By the time of the invasion of Iraq in 2003 both had been replaced in service by the M-1 Abrams and AH-64 Apache.
Early on, when Matt Ocre is walking to infirmary to get the cast off of his hand, he passes several M60's being loaded. Later after getting the cast off he talks to some guys from his squad, telling them: "Did you guys see armoreds rolling out? ... And I saw Cole loading the Abrams"
Definately not Abrams, but M60's.
The beard of Captain Syverson (Henry Cavill) should have been shaved off and his hair cut. While Special Forces personnel are given special dispensation while in the field or on special assignment (they are either too far from base for anyone to care or required to fit in with the locals), that does not apply when they are assigned to a regular unit. As Captain Syverson was in charge of what amounted to a repair crew, his hair should have followed standard military protocols.
The turrets of the Humvees in Ocres unit include protections (armored shields, ballistic glass viewing ports) that were not in use at the time of the invasion of Iraq in 2003. In point of fact those came about as a result of the experiences of American troops both during and after the invasion.
An MRAP (possibly a Buffalo or Cougar) appears in the motor pool during the first scene which is set in 2003, MRAPs were not in common use until around 2007 onward by the US military.
In one scene, a soldier is seen using a Leatherman Skeletool to work on his rifle. This model of multi-tool did not exist until 2007.
According to Army Regulation 600-63 smoking is forbidden in all military vehicles and aircraft. Near the beginning of the film soldiers are seen smoking cigarettes inside the Humvees. They should not be doing this especially an NCO like Chutsky whom should especially know better.