When driving backwards through the woods, the audio for the engine is revving at far too high revolutions as to drive so slowly. Additionally, it goes up and down out of sync with the driving displayed.
In the opening fight scene in the diner, after Mallory takes Aaron's pistol she racks the slide to charge the pistol (i.e., to load a round from the magazine into the chamber). In semi-automatic pistols, this is only necessary when the chamber is empty and is done automatically after firing each shot. As Aaron had already fired two shots before Mallory took the gun, the chamber would have been full (and, in fact it was, as an unfired round was ejected as soon as Mallory pulled the slide back).
During the fight scene between Gina Carano and Michael Fassbender, the gun between the mattresses can be seen sticking out halfway when he throws her on the bed, but when she reaches for it moments later she needs to dig for it under the mattress.
When Mallory finds out she has a tracker in her backpack, she runs out of the store and across the street into a hotel. As she runs up the stairs she throws a lot of stuff into the stairwell to slow her pursuers. But when the SWAT team comes up the stairs there is nothing there anymore.
When Mallory & Scott are driving, she tells him to have a drink of water in her backpack. She wants some too, but has to have him pour it in her mouth because of an injury to her arm. However, just minutes later while running from law enforcement, she is backing up at a high rate of speed, her bad arm is extended and gripping the passenger seat tightly.
When Mallory and Aaron fight in the diner in the opening scene, Aaron attempts to shoot Mallory at close range while she is lying on the ground. Immediately after the shot, the powder burn from the muzzle blast is clearly seen on the floor of the diner next to Mallory's head. However, there is no other damage to the floor as an entering bullet would have made, revealing only the damage that a blank cartridge would cause.