Agree with everyone else that not everything is 100% accurate, but at the same time, it's a movie not based on an actual story. It isn't trying to be 100% accurate. More importantly, it's a decent general overview of a grunt's story in Iraq at the time.
The problems I do have are the writing. The beginning is pretty good, but once it gets to the schoolteacher being killed it starts falling off. The ending is also pretty poor-so dude get's into one battle and suddenly he's going home, and somehow he still managed to get the most closure of any main character. Again, it's not in any way terrible, but nothing is memorable. Even if he's a blank slate, the MC is still supposed to have something.
Overall, if you're expecting something over-the-top or looking for something to scrutinize for total accuracy, look elsewhere. If not, then give it a watch, but don't expect anything crazy.