Liberty Division, the 77th part of the Lost Battalion, took Hacksaw Ridge in Okinawa in WWII.
MAJ Charles Whittlesey (later promoted to LTC) was a pallbearer, along with Alvin York, for the interrment of the first Unknown Soldier in November, 1921. Two weeks later, Whittlesey booked passage on a boat to Havana, and committed suicide the first night out by throwing himself overboard. He was said to be haunted for the rest of his life by the incorrect coordinates resulting in the friendly fire bombardment of his Lost Battalion.
The doughboys in the film are equipped with the US rifle of 1917, aka, the "American Enfield" or "Eddystone" rather than the iconic M1903 Springfield. This was a good detail, because it's correct- due to manufacturing delays, the majority of doughboys were equipped with the M1917, an adaptation of the British Enfield, rather than the more famous "-03 Springfield."
The name "Mulcahy" is carved above the Major's office in the trench. The director of the film was Russell Mulcahy.
The passage that Whittlesy quotes to comfort the dying soldier with the blood-soaked Bible is Psalm 71:1-5, KJV.