Factual error: Chris Kyle did not make Chief after his first deployment. He made Chief during his fourth deployment.
Factual error: When Taya is watching TV and sees the first of the Twin Towers get hit by the suicide plane, she calls to Chris and they watch it together. Chris was born in 1974 and it states he enlisted at 30 which would've been 2004. The bar scene where Taya and Chris meet was after he completed his BUDS training and sniper school. Which, if was timeline accurate would have been 2004 or 2005. Therefore they could not have watched the events of 9/11/01 unfold together on TV because the wouldn't have known each other yet.
Suggested correction: Chris Kyle joined the Navy in 1999. Not 2004. His book American Sniper does say he was at Taya's house on 9/11. He was summoned back to the base and got caught speeding. Luckily the officer decided to not ticket him.
Factual error: In the first scene when Kyle is doing over-watch for dismounted infantry, an Iraqi is shot and his body falls from the rooftop, startling a soldier. The report is heard first, the a hiss of the incoming shot. It was cool that they tried to make the hiss, but it should have been first, as the bullet is supersonic, and arrives before the report of the gun is heard. Pretty egregious error for a sniper film.
Factual error: When Chris Kyle talks to his wife from Iraq over the phone as she exits the hospital, it appears to be roughly the same time of day in Iraq and in Texas as the scene cuts between shots of Kyle and his wife. Given the time difference, if it were 12 noon in Iraq as Kyle is speaking, it would be 5 AM in Texas as Kyle's wife is speaking. The similar time of day is simply not possible.
Factual error: Throughout the training (sniper) and other times during the movie, shooters react like the rifle has a heavy kick, which they don't.
Factual error: The ranger is wearing an airborne tab above his 2nd Batt patch. They do not wear the airborne tab, rather they just wear jump wings. (01:39:38)