The MPs are shown as working the case. In fact, the death of a Marine would be investigated by the Naval Criminal Investigative Service (NCIS).
The movie has the Marines taking total control over the investigation. Actually, since the death was discovered off base, the civilian police would have taken the lead, Naval Criminal Investigation Service (NCIS) would have added their services with the Base MP kept apprised of the progress.
When Fincher is holding the gun on the murderer, ready to shoot, the music swells and finally he lowers the gun. At that exact moment, the murderer lowers his hands and relaxes. But since Fincher is behind him, he would not know the tense moment was over. He wouldn't drop his hands or relax until after Hailey, in front of him, reacted.
They keep saying that the base is in Albany pronounced like it is in New York. In Georgia, the accent is on the BANY not on the AL. That's just what the Georgia people call it.
USMC Lt Young refers to Fincher Garland as a former Marine. No active or prior service Marine would ever refer to another Marine as a former Marine. "Once a Marine, Always a Marine."
Hailey says the bullet wound was too small for a 38, and asked if it was a 9 millimeter. The bullets for both of these are within 2 thousands of an inch. A 38 caliber bullet at .357 inch is .002 inch larger in diameter than a 9mm, which is .355 inch. Due to this small difference, a 9mm round can be fired from a 38 caliber gun barrel and vice versa. Taurus made a gun, the 692 revolver, that could fire 38 special, 357 magnum, and 9mm via use of different cylinders. This difference would be undetectable to the human eye looking at a bullet wound.
They repeatedly mention that Fincher Harland is a Marine. When they are talking about the Semper Fi email servers, Fincher says, "Semper Fi. It's the Marine's motto, it means always loyal." Semper Fi is the shortened form of Semper Fidelis, meaning Always Faithful, not loyal. A Marine would never make that mistake.
Finch and the Marine MPs use the term AWOL (Absent Without Leave). That is a term used by the Department of the Army and Department of the Air Force. The Department of the Navy (which includes the Marine Corps) uses the term UA (Unauthorized Absence).