Other mistake: After the shoot out at night the American forces are faced with a group of hostile locals, and the team are told to pull out and get in the vehicles. As they drive off we see a back shot of them sitting on the back of the one of the vehicles, but on the right hand side you can see a backpack and part of an American soldier, did they just leave him? (01:12:50)
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.
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.
Continuity mistake: When the two Humvees are leaving, they get intercepted by a green Renault 12 which they shoot up and ram. The Humvee after hitting the Renault then hits a wall and suffers damage. After the Humvees come to a halt some moments later, the wall damaged Humvee is now pristine again.
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.
Continuity mistake: While Chris is waiting for his baby girl to finish being breast-fed, he talks to his wife and puts heaps of stuffed animals, including the really big one that he won, for his then girlfriend/later wife, into the cot. When he puts the baby down into the cot, there's not a stuffed animal to be seen.
Other mistake: When Chris Kyle is celebrating his daughters Birthday party at the end of the movie he comes from inside the house and out to the back yard, While he is talking to his wife and watching a dog play with his son, after a minute it looks as if the dog is attacking his son and he gets up to stop the dog. As he gets up you can see that his pants are wet and that he has grass stains on his knees from the previous takes. During the actual scene he is on his knees with a belt to stop the dog when his wife yells at him to stop.
Character mistake: While watching the events of 9/11, the broadcaster notes that the "south tower is collapsing" while footage of the North tower's later collapse is showing. The south tower fell first, 29 minutes prior to the north tower. (00:22:25)