Continuity mistake: When Reacher arrives at the shooting range it's hot and sunny. When he walks down the driving range it's overcast and looks like it's been raining with a slight mist coming in. When he looks back down the range, cut to the owner and shooting scene and it's hot and sunny again.
Continuity mistake: When Sandy is going out she puts on bright red lipstick. When the police find her body the lipstick is gone.
Continuity mistake: In the car chase in Jack Reacher's car, there's a sticker with numbers on it - first it said 5 12, then 7 12, then 9 12, and from the shots within the car it doesn't show the sticker at all.
Continuity mistake: When Jack reverses aggressively out of the motel car park onto the road, he steers the car to his left and drives down the road, not leaving any tyre marks. In the next shot, the police cars exit the car park sliding out onto the road to their right, following tyre marks which have magically appeared, presumably from a previous take of that action.
Other mistake: In the scene where James Barr is shown shooting the four men during the war his rifle movement is inconsistent with where the targets were. He took aim at the man furthest away in a line. His rifle would have to move down as he shot each person moving down the line. Instead his rifle moves down then up and up again etc. Even if the targets decided to run after the first shot the rifle movement is inconsistent.