Whenever Col. Winters talks on his radio, you can hear a hiss of static after he releases the button (breaking the squelch.) You only hear this when you are receiving a message on any radio, never when you are transmitting.
When General Irwin and Winter are talking about the battle of Shiloh, Irwin says that Grant lost 13.000 men. That number however includes men killed, wounded, captured or missing in battle. The real number of men that Grant lost (as in dead men) is 1,754.
When Col. Winter sees the trebuchet, he says he has "no idea" what it is, but seconds later correctly calls it a trebuchet. Any graduate of the West Point US Military Academy should be easily able to identify one.
After Yates flies the helicopter into the gun tower, the helicopter begins to flip and you see that the door is no longer on Yates's side, but when it comes to a halt, not only is the door there but it's closed.
It was an error to have Irwin be a 3-star general. 3-star and 4-star generals hold their ranks temporarily, as long as they occupy a 3-star or 4-star position. When they are transferred from one 3- or 4-star position to another, the President must re-nominate them for Senate confirmation. If an officer is relieved (fired) from one of those positions, he reverts to 2-star by operation of law unless awaiting retirement (and then only for 60 days). Irwin was court-martialed, so the Army certainly wouldn't keep him in a 3-star slot. They'd relieve him and he'd go to court-martial as a 2-star. See 10 USC 601.
Colonel Winters and Captain Peretz's rank and branch insignia on their BDUs (Battle Dress Uniforms) are attached incorrectly. On those now defunct uniforms, and different to enlisted personnel, Army officers wore their ranks so that the insignia was perpendicular to the front edge of the collar not centered on the V formed by the collar.
There is a common misconception that the law requires actors portraying military personnel to wear the uniform improperly (so as to not be "impersonating" military personnel). This is simply not so. 10 U.S.C. 772(f) does authorize the wear of an armed forces uniform by an actor in a theatrical or motion picture production "if that portrayal does not tend to discredit that armed force." SCHACHT v. UNITED STATES was a Supreme Court case in 1970 which found the preceding quote unconstitutional. As such, actors may wear the uniform in a theatrical or motion picture production without fear that it must reflect well on the military. Short version: Any movies which depict improperly worn uniforms can't use this excuse. They just screwed up.
During the first firing of the trebuchet, the filmmakers reversed the image. It shows Tower #4 and the smokestack behind the trebuchet and it firing the stone to the left. If this was true, they would be shooting the rock away from the admin building.
The goof item below may give away important plot points.
When Irwin is delivering Aguilar's eulogy, all the men are standing at attention. There is a close-up of Winter through his office window, and you can clearly see the reflection of the men dispersing. In the next shot, they're all still at attention.
When Aguilar gets shot with the rubber bullet, we clearly see the impact toward the rear of his head (shown by a spray of perspiration). As he drops, we see no impact wound on his left temple. In the next shot of him laying on the ground, there is an obvious impact wound to his left temple area.
Towards the end, after Irwin has been shot, behind Yates' shoulder you can see men saluting the flag. However, it is only in the subsequent shots after first one then another of the main characters realise that the flag is up and start to salute that the other ranks follow suit and salute.