When Theron enters his room and sits on his bed after the snipe hunt, there is a telescope pointing to the left in the background. Immediately after, his father Wade enters and the telescope is now pointing to the right, which he then turns back to the left.
When Rafe approaches Libby to ask her (on behalf of Theron) to the upcoming dance, the opening shots are clearly filmed outdoors at a real house. When the shot changes to Libby's perspective as Rafe leans over the hood, the lighting changes to indicate what is clearly an indoor shot on a soundstage. The amount of water and the lighting on the hood also changes compared to the original shot.
Theron is shooting cans off a fence for target practice. However, every time he hits a can, it shoots straight up in the air instead of backwards. In addition, little puffs of bluish smoke are visible - probably indicating a small charge of gunpowder was used to propel the cans.
The wild hog appears to be a painted domestic pig with phony tusks attached. A real wild hog would never be that fat either.
Theron is looking for the person who shot his father, and chases him in to the woods. Though this scene is during daylight hours, as Theron walks through the woods he casts two shadows.
When Rafe and Theron start the hunt for the boar, they let the dogs loose and then they run down the trail after them. As the camera pans to follow their movement, an obvious puff of cigarette smoke from a crew person off camera drifts into the shot from the right.