Factual error: When Reacher is talking to Major Turner's lawyer Col Moorcraft he is wearing Military Police Corps insignias (Crossed Pistols) on his uniform, not the insignia of the Judge Advocates General (JAG) Corps (Half Wreath with arrow and sword) which is what an Army lawyer would be wearing on his or her uniform.
Factual error: On the plane Major Turner states she has been in the Army 10 years. She means after she graduated from West Point. Even accounting for super fast promotions, if she has been in for 10 years from age 18, she is too young to have had 3 promotions to Major and have the command she does in the movie. Even after 10 years out of the academy, this would be very quick.