Other mistake: When the soldier says "Sir, she is trying to access the system" we can see the name she is typing in as she is typing it. This isn't possible unless they have a remote desktop connection, which they don't because they don't know where they are at. They are also using MacOS with a Windows background which isn't impossible but it is kind of weird. (00:29:15)
Continuity mistake: When Jack tosses Samantha's phone out the car window (when leaving the prep school), it breaks into three pieces, two on the walkway and one onto the grass. When The Hunter walks up to the phone, all the pieces are near each other on the walkway, and they are on the other side of the walkway than the two pieces originally landed. (00:47:35 - 00:49:15)
Revealing mistake: When the leading hitman jumps from the balcony you see him land on a rubber mat.
Other mistake: Major Turner tells Reacher that the men Parasource killed were shot twice in the back of the head. During Prudhomme's telling the images show the downed soldier on his back. The other is shown being shot and falling on her back. Then the two kill shots each. They couldn't have been in the back of their heads.
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.
Continuity mistake: In the diner at the end of the movie Sam's hair is behind her ear, then over her ear, then behind her ear again.
Continuity mistake: The small wound below Jack's left eye increases and decreases size through the film.
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.
Continuity mistake: In the first movie, it was explicitly stated that Reacher was sort of a ghost who was born in an army base somewhere and spent his entire career abroad; he entered United States "for only the second time in his life" (the first being West Point), to disappear living a life off the grid. In this movie, it turns out he had a cozy office (with the same desk as Major Turner's), and was stationed in DC.
Visible crew/equipment: Towards the end of the film, when Sam runs back for her hug, a red haired woman in a purple coat appears briefly on the right.
Character mistake: Jack breaks out of prison and uses Military Police Car L67. When the General discovers this he radios to all units and says S67.
Continuity mistake: In the beginning in his first fight Jack gets a wound on his right cheekbone which disappears in the next days.