The movie claims that the Provost Marshal is "the closest thing we have to an investigator". Not only was there a Criminal Investigation Divison field office in Panama at the time the movie was set in, the Provost Marshals office has it's own Military Police Investigations office.
When Sgt. West comes into the bunker, he traps Mueller, fully dressed, against the support beam with the knife. However, Mueller, without his shirt on, is also the first one he stabbed. Mueller is simultaneously shown lying dead on the ground shirtless, and pushed down, wearing a shirt.
Just before Hardy and Osborne get out of the car to go and see Kendall in Hospital, Hardy removes his jacket and throws in to the back on the car. Once inside the hospital, Hardy has his Jacket on again.
In the scene where Pike is climbing the cliff and Sgt West is challenging him to use his brain, there's a moderate, steady rain shower. When Sgt West throws his pack down the cliff, there's no rain as his pack is shown falling.
Osborne states that US Army records do not show race, which would make it very easy for Pike and Dunbar to switch dog tags as shown. Not only is this completely false, but by 2003 basic screening requirements for anyone enlisting in the US Army also included fingerprinting, dental x-rays, and providing a blood sample for DNA records. Even if both Pike and Dunbar had enlisted prior to this requirement going into effect, as graduates of the Ranger School and current students in the Jungle Warfare School they would both have had to undergo a background investigation for a security clearance, which would include fingerprinting at a minimum.
After Obourne kills Col. Styles, she is interviewed and then proceeds to follow Hardy back to Section 8, where she draws her service weapon and threatens to kill him. In actuality S.O.P. of any law enforcement agency since the days of the old west, would be to confiscate the alleged murder weapon as evidence.
At the movie's beginning, we're told that the training exercise happens on November 2nd, "The Day of the Dead". The interrogation probably happens the same day or next, but when we meet Tom Hardy he is being told by a passing girl "It's Carnival, come on". Carnival happens before Lent, typically in February.
At the beginning of the movie, one of the revelers tells Travolta's character that it's Carnival. Throughout the movie, people refer to the hurricane to explain the bad weather. Carnival usually happens in February, which is not hurricane season (it's smack in the middle of the off-season for hurricanes).
Ranger Training is conducted by the Ranger Training Brigade, who wear a scroll patch similar to the 75th Ranger Regiment. MSG West, their trainer, was wearing a patch from the 193rd Infantry Brigade. The Jungle Operations Training Center in Panama was not part of the US Army Ranger School or the Ranger Training Brigade, but did have administrative ties to the 193rd Infantry Brigade.
Right before Kendall talks about being the victim of a hate-crime during his narration, strobes that generate the lightning flashes can be seen firing above in the trees as Castro is shooting at targets.