After the bar fight, when Reacher is in a jail cell, he is lying with his head towards the door, basically facing the wall. Reacher, as described in the book series that includes the book (One Shot) upon which this move was based, would never have his back to the door if he had the choice.
Jack tells Helen that Barr "makes his own bullets". Someone with his knowledge of firearms would say that he reloads or that he makes his own cartridges, Barr reloaded cartridges; the bullet is just the part that exits the barrel.
When the coin is originally placed into the parking meter, the limit on the meter is marked as 30 minutes.
Later when the police find the meter it reads 10 hour time limit.
When Jack then goes back to the area in the car park where Barr set up to fire the meter once again reads 30 minute time limit.
During the car chase, after Jack finds Charlie in the alley, they speed away from a parking garage entrance that's lit up with blue lighting. About twelve seconds later, Jack is drives away from that building again, without moving any farther down the alley.
Car chase: Jack's car lights: Rear: Left light broken/OFF. But when Jack leaves the car at the bus stop, the car keeps moving with both rear lights ON. Front: orange light on the left (driver's perspective) is broken/OFF. This changes from being off/on continuously.
The "highway bridge" the sniper should have used is the I-279 bridge. It is shown to have the sun behind it (west) in both the original shooting and the hypothetical discussions. This would mean it's evening (sun is low in the sky, during summertime) - not the morning, as indicated by the shooter's watch and the victims' stories.
At the end of the movie, when Helen is speaking to James Barr in the hospital, she advises him that the conversation is classed as privileged - meaning it is strictly between Helen as lawyer and Barr as client. However towards the end of the conversation, the camera pans rounds and reveals that District Attorney Rodin is in the door way. As DA Rodin was prosecuting Barr, this would make his presence with Helen's knowledge a violation of the lawyer/client privileged conversation.
Early in the film, Jack Reacher says that there is a bus stop "3 miles away" and that he can "walk there in 24 minutes". That is a speed of 7.5 miles per hour, far faster than walking (unless Jack Reacher is a world-class race walker).
Early in the film, Helen tells Jack that their conversation is attorney-client privileged. No competent attorney would make that claim, as discussions with non-party witnesses are not at all privileged.
At the range, Reacher and Cash are looking at the target after Reacher puts 3 rounds through the "X" ring, The holes are perfectly round and cleanly cut. A pointed rifle bullet leaves a ragged hole and would never leave a perfectly round hole through a paper target.
When Barr is shown shooting at Hinge Creek (intercut with Reacher firing a different rifle), and at various other points in the film, he obviously jerks the rifle in anticipation of the recoil-- something a trained ex-military sniper would never do.