Continuity mistake: After Ellis and his mom are stopped by the Troopers, one of them holds a clip board with Mud's picture on it and finger prints. As he is showing it to Ellis, the close up shows his fingers over the finger prints as he is holding it one-handed. Then in a further shot, his fingers are suddenly holding the board about 2 inches above the finger prints.
Continuity mistake: After telling Ellis the bonfire is for good luck, he and Mud begin walking back towards Ellis' boat. As Mud says "You don't know his story" they are in shadows of trees about to walk out into the clearing, but there are bushes in the way. The angle cuts with Ellis saying "I don't care" and suddenly they are out in the sunlight in the clearing, and the bushes they were walking up on have vanished.
Continuity mistake: Once Mud reveals who he shot and asks for Neckbone and Ellis to help him get the boat out of the tree, Neck asks for the pistol in return. Mud reaches around his back and puts his hand on the handle of the pistol tucked in the back of his jeans as he begins saying his shirt and pistol are the only things of value he has. It cuts to a close up, and suddenly his hand is on his hip and he reaches for his shirt, then back around to his pistol again.
Plot hole: Just after Ellis tells Mud about Carver beating up on Juniper, he gets mad and punches the ground and then they start gathering up the stuff Ellis and Neck brought to take it to Mud's boat. They are right on the shore of the river and can see in most directions. Two people are sitting in boats out on the river, just watching Mud and the kids. Very much in visible range and they stand out, one of them even wearing a red shirt. Yet Mud, despite being on the run from cops and bounty hunters, never even notices the two very obvious boats out in the water. If he's running for his life from that type of people, he would have an eye out for them. Not even Ellis and Neck notice them and they just came on the river, and one is Neck's Uncle Galen.
Factual error: Ellis and his mom come across a roadblock and police checkpoint of State Troopers checking cars for Mud. The Arkansas State Trooper that comes up to the window is wearing the wrong uniform. His badge is wrong, and his shirt is wrong. He has one of the cloth badges on his right shoulder, but it is the wrong shape for State Troopers. And he has an American flag on his left shoulder. Arkansas State Troopers have the cloth badge on both shoulders, not an American Flag.