If Billy went barefoot most of the time, especially on rough and rugged terrain, the skin on his feet would have become very tough and callused, and he likely wouldn't have felt the dogs licking his toes.
The visible boom mics are a result of the home video transfer. The film was shot "open matte" and cropped to an aspect ratio of 1.85:1. In subsequent video releases, the entire 1.33:1 frame is shown.
Mr. Kyle says "Billy's hounds treed three coons." They actually found four; they'd gotten the first one treed before they trapped the other three coons in the second tree.