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)
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: Escaping from prison Turner wears a T-shirt. In the car later she wears a combat shirt. And after that a T-shirt again.
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.
Continuity mistake: The small wound below Jack's left eye increases and decreases size through the film.
Continuity mistake: When Jack Reacher and Colonel Bob Moorcroft are talking in the park while walking, they pass by a guy seating on the bench reading a newspaper. In the next shot from a different angle they pass the same guy again.
Continuity mistake: In the beginning in his first fight Jack gets a wound on his right cheekbone which disappears in the next days.