When Briscoe Darling offers Andy a guitar, he says it only has five strings. When Andy plays it, the guitar clearly has six strings.
When walking to the Darling house from the patrol car, Andy's pants cuffs are hung up on his boots. When the angle changes as he steps up to the front door, his pants legs are hanging properly around his boots.
With snoring so terrible in the Darling residence, Andy and Barney never consider sleeping in their patrol car (or that, once asleep, nothing can wake Barney but snapping fingers).
Andy decides to stay overnight at the Darlings with Barney. There's no way for him to send word and let Aunt Bee and Opie (or anyone in town) know this, leaving his family to fear the worst when Andy doesn't come home at night.
Andy determines to find the remote Darling mountain residence by the sound of their music, even though he drives on a wide, well-flattened road and even though Barney points off and says to try "that one up there" (either a house or a roadway, not shown, that would seem to be clearly visible and among others).
Earnest T. Bass throws a rock with a note attached to it, but in "The Education of Earnest T. Bass", it is revealed that he is illiterate, except for the ability to read a few words: "no hunting", "no trespassing", "beware", "open" and "closed" and "no credit".