Barney tells Opie that he used to write for the Central High newspaper. In the episode "Class Reunion" (season 3, episode 19), Andy and Barney sing the song from their high school: Mayberry Union High.
Aunt Bee is digging through her purse while she and Barney gossip about Harold Grigsby and his young wife. The purse goes from being open and underneath her crossed hands as the Grigsbys approach, to closed and hanging from her left wrist in the immediate shot as they pass by.
Opie and Howie are printing a school newspaper in Howie's garage. When Opie removes the last copy from the printing press, you can easily see that the paper has no printing on the back. Opie puts this sheet onto a stack of sheets which he then puts on top of hundreds of other sheets in a child's wagon. They then take the wagon and head out, we assume, to deliver the newspapers. After that point, all the boy's school newspapers we see throughout the rest of the episode are printed on both sides of the paper. Even the next week's newspaper that Andy, Barney, and Aunt Bee find in the town dump has printing on the back side.
Sheriff Andy Taylor and old Burt Mustin are sitting on a sidewalk bench in front of a store display window discussing the apparent length and dryness of the preacher's sermons. Young newspaper reporter Howie is eavesdropping nearby. There is a slight breeze blowing that is enough to move Howie's cowlick. The revealing mistake is that the breeze is also moving the drawstrings on the blinds inside the window and moving some loose packaging on a product displayed inside the window directly behind Burt Mustin. This reveals that there isn't any glass in the store's display window.