Several times throughout the movie, Captain Stone notifies next of kin of deceased soldiers without first getting positive confirmation that they are, in fact, the soldier's next of kin. Casualty Notification Officers are required to make sure that the person they are addressing is actually the next of kin before making notification. This is not a mistake that a professional like Captain Stone would make.
Staff Sergeant Montgomery tells the recruiting sergeants in the mall to take a walk, and one of the sergeants replies, "Yes, sir." Only officers are referred to as "sir." A sergeant addressing another sergeant who outranks him would simply say, "Yes, sergeant."
Ben Foster isn't wearing a Combat Infantryman Badge when notifying Steve Buscemi but has it adorned at the next notification of Olivia Pitterson at the clothesline. There shouldn't be an exception to wear his dress greens without it. Also it is made clear that Foster served as a mechanic in Army, and never served as an infantryman. Combat Infantryman Badges are only awarded to infantrymen. Foster would have been awarded The Combat Action Badge.
Montgomery's dress uniform is lacking the blue infantry cord and the blue infantry discs under the BOS pins. While Montgomery was not currently attached to an infantry unit he was still awarded the MOS of Combat Infantryman, this entitles the soldier to wear the blue cord and discs on the dress uniform indefinitely.
Montgomery wears an armor crest as his branch insignia and also wears a Combat Infantry Badge. Since his branch insignia crest represent that he is an armor crewman and not infantry, he should not be wearing a Combat Infantry Badge. Only the infantry can wear a Combat Infantry Badge after being awarded the badge while in combat.
When notifying Olivia of her husband's death, Captain Stone tells her, "You're listed as the NOK on your husband's forms." NOK is an acronym meaning "Next-of-Kin". Casualty Notification Officers are instructed not to use acronyms when making a notification, as the Next-of-Kin might not understand them.
SSG Montgomery should have at least two service stripes on his left sleeve, in addition to the missing Overseas Service Bars. Each service stripe denotes 3 years of service and he'd likely have at least 2 of them.