I really enjoyed the movie and recommend it
Adam made good points. The end was fuzzy. A read of the book would be a great complement to evaluating how close the movie depicts reality. One may also want to read Victory Point
which contests some of Marcus Luttrell's telling. Personally, I see Luttrell as an absolute hero and the differences aren't attempts to obfuscate, but differences in perspective.
Some minor inaccuracies off the top of my head I think I saw in the movie:
-The SEALs used an EMBTR as their primary radio vs. the radio depicted in the movie.
-The helmets they initially wore on the mission were non ballistic (they have holes in the top for ventilation). That doesn't seem right. For training they'd be fine but operational? I think not.
-When they were debating what to do with the shepherds, they didn't consider taking them with them. On the other hand they didn't necessarily show how difficult mountainous terrain is and leading tied prisoners through that type of terrain might haven't have been an option as well as the risk that they would yell for help or compromise them in some other way.
-The death of Michael Murphy wasn't depicted as described by Luttrell in a recent interview.
-Rangers rescued Luttrell in reality. Their uniforms, helmets & body armor weren't accurate for 2005.
-The Air Force Pavehawk that eventually rescued Luttrell made a very precarious landing on the edge of a cliff.
-The surviving SEALs didn't watch the QRF get shot down.
-The Spectre didn't provide support during the day.
One realistically depicted detail was the lack of use of automatic fire by the SEALs. I REALLY enjoyed that attention to detail because most military movies fail in this area.
The other interesting detail is real world considerations impact your support as was depicted when the Apaches had to support other troops in combat.