Rachel leaves Davis' glass of water half full but in the next shot when Davis goes to the kitchen, the glass is completely full.
When Jimmy trails Clinton in his car they travel quite a distance before arriving at the mill works. This includes crossing a bridge (presumably over a river). When Mitch realises Jimmy is in trouble he runs at speed to the mill covering the rather long distance in a much shorter time than the two drivers did and with no indication of crossing either a bridge or a river.
After Brokden escapes, saying Davis is going to kill his family, Det. Kanon says to get a unit to Brokden's house. Yet she is the first one to get there, alone, before sirens are heard from the other police that are on the way,.
Mitch supposedly has an injured arm in a sling but carries his baby for a while single handedly with that broken arm. Because of how badly Jimmy had been tortured, enough time could have past by the time Jimmy comes to visit Mitch and his wife that Mitch's arm might still be sore enough from being shot to wear a sling, sort of like a security blanket, but he can still use his arm. Also, it is not said that he has a broken arm.
At the end of the movie, Jimmy walks with the aid of a cane and has a limp but when he walks into the house, he doesn't need the cane anymore and walks fine.
Brokden puts his handkerchief over the phone's mouthpiece to disguise his voice, but he doesn't wipe off his fingerprints.Nothing is said by the police that they even checked for fingerprints on the phone.