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).
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 reciting Reacher's bio to the DA, Emerson states that Reacher had served all over the world, but had never been in the U.S. until leaving the Army. This is clearly contradicted by the history given in Lee Child's books, but it is a particularly glaring error because the next movie made in the series is "Never Go Back." The plot of that book and movie relies heavily on Reacher's prior service as an MP stationed in Washington, D.C.
When Reacher is at the range he shoots right handed. When he first shoots at the quarry he shoots left handed. When he puts the gun to Charlie's head it's right handed. When he shoots Emerson hes left handed.
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.
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.
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.
When Jack Reacher is at the office of the shooting range a semi-automatic M14 rifle is shown. He is to use that to put three bullets in the center of the target to maybe get a answer to his question. In the next scene at the shooting range he is not using the semi-automatic M14 but a repeating rifle.
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 Jack Reacher pulls out the Camaro's registration, it erroneously reads "State of Pennsylvania." Like three other states (KY, MA, and VA), Pennsylvania official designates itself as a "Commonwealth" not a "State."
When Jack is answering Prosecutor Rodin about what he knows, he says "there is a bus station 3 miles away and I can walk there in 24 minutes." Even the fastest walkers can't cover 3 miles in 24 minutes. That pace is a run or jog at best.
Though it may seem anachronistic for Barr/the sniper to use the M-14/M-21/Springfield M1A as his weapon of choice, it's origins trace back to the M-1 Garand from WW II, the weapon, in one form or another continued to be used by units of the US Army and Marine Corps during the wars in Afghanistan and Iraq as a sniper/designated marksman weapon.
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.
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.
After police finds Alexia Fast's character body beside a dump, there is a close shot at her pulsating throat artery which mistakenly reveals that she's still alive although her character is dead in this scene.
The shooting was supposed to have taken place in the morning, from the parkade on the south side of the river, across from PNC Park. When the emergency team arrives, the van comes from the west, casting a shadow in front of the van (east)- which would make it evening.
The goof items below may give away important plot points.
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.
As they are loading Sandy's body into the ambulance you can see she is on the stretcher backwards, against universal ambulance procedure. Her feet are even lifted up in the air and her hair is spilling out from under a sheet.
Near the end of the final shootout battle, Emerson shoots at Reacher a couple of times before Reacher kills him. When Reacher enters the room, he motions to Helen to hand him Emerson's gun, which was a Glock handgun. When Reacher is taking it from her, you can clearly see that the trigger is locked to the back of the trigger guard, indicating as if the gun was dry fired and empty. Since there were no indications of anyone clearing the firearm or dry-firing it, the gun's trigger should have been in the normal, ready-to-shoot position as there was another round chambered.