Revealing mistake: When Chris and a companion are on a rooftop in the midst of clothes lines with sheets hanging to dry, all the sheets have creases indicating they had been recently unfolded or removed from original packaging before being hung on the lines.
Revealing mistake: About 3/4 through the movie, Bradley Cooper and his wife are talking in a bedroom or nursery. He takes his daughter and holds her - the baby is clearly fake.
Chosen answer: Chris has "shooter's strawberries" on his elbows, which are red callouses caused by lying in the sniper's position for long periods. He notices the same marks on the elbows of the father, and realizes that he too is a military sniper.
Sierra1 ★