Character mistake: The new sheriff ("Alice") told Rayburn that she has only been sheriff for a couple months and was still catching up on active cases. Rayburn replied, "Yeah, my daughter's case is far from active." The sheriff then told Rayburn, "My training is very different from the officers around here" - meaning college-educated (Ivy League?), more professional, more effective, and modern. Despite this, some of the sheriff's actions (e.g, walking unannounced into suspects' houses and/or without a proper warrant; questionable "probable cause"; shooting Rayburn to protect her brother) fell far short of the ideal. Perhaps most significantly, the sheriff gave Rayburn a warning shot and told him not to kill Dr. Boone... then she stood back and merely watched Rayburn push Dr. Boone into the pitfall and close the doors while knowing the doctor was severely injured and dying. These things do not show her purported superior training. (00:21:43 - 01:25:34)
Other mistake: Rayburn pulled an arrow out of his chest - and without much blood gushing out. The rather small amount of blood on the towel and Rayburn's ability to go about business as though he had not been injured is unrealistic and absurd. (00:27:00)