The sex video breakup scene is actually a well-known legend that has been circulating in the American military since the late 1940's, and actually does happen. This is known as getting "Jody'd/Jodied" And is coined in several military cadences during marching/running. In the early days, 'Joe the Grinder' was the original term, later shortened to 'Jody' as this made it easier to rhyme with and use in cadence recital. This is a very large fear of many military members, most notably during deployment. The usage of the term 'Jody' in cadence is to normalize the fear that you have chosen this career/job path and have committed to it, as a reminder that because of your choices, their can be consequences from it outside of the military itself. The 'Jody' scenario, has led to numerous instances of injuries, arrests and actual loss of life, not excluding self harm/death and murders.
A great deal of the dialogue is improvised. This was a deliberate choice on the part of Sir Sam Mendes to be a little more organic after the stylization of Road to Perdition (2002).
The burning oil wells were all computer generated. The oil that appears on the soldiers' faces was a concoction made from molasses.
Jake Gyllenhaal was convinced he had blown his audition, especially after several months passed and he hadn't heard back from Sir Sam Mendes. An impassioned message Gyllenhaal left on Mendes's voicemail swung the decision in his favour.