Ensemble Darkhorse: Andy and his family were meant to be the focus, but Barney stole the show.
Hilarious in Hindsight: All the times the male characters wished they could be as good with the ladies as Rock Hudson... Rock Hudson was later revealed as a homosexual. In one episode, Barney says that he learned how to sweet talk ladies by watching "all those Rock Hudson movies".
Also, in the episode "Man In a Hurry", the titular character happened to be named Malcolm Tucker.
Idiot Plot: Numerous episodes would have been resolved in under a minute had someone decided to tell a slightly uncomfortable truth rather than try to spare someone's feelings. "Dinner at Eight" is probably the worst offender, when Andy was 'forced' to eat three spaghetti dinners in one night and be blamed for being late to one of them, when all he had to do was admit he didn't get a telephone message. Or call when he did get the message and say he was going to be late. Or if the host had called and made sure he had gotten the message. Or the host called when he didn't arrive and ask what had delayed him.
Replacement Scrappy: Warren Ferguson. The guy didn't have an ounce of what made Barney so funny. The fact that he tried to fill Barney's role, but ultimately failed, is what made his character particularly unfunny.
Seasonal Rot: A pretty serious case. After Don Knotts dropped out of the show after the fifth season to pursue a film career, the series went on without him for three more years. Most fans dislike these episodes (easily recognized because they were shot in color) for being unfunny and moralistic. Without Barney to play off of, Andy loses much of what made his own character funny, and he becomes a rather solemn grump.
Also, the sudden addition of new neighbors in Mayberry, such as Howard Sprague and Emmett Clark, really didn't help matters much either.
Values Resonance: A clip of Andy erasing a recording Opie made of a conversation of a suspect and his lawyer made in secret while defending the right to privacy and attorney-client privilege has been making the rounds on YouTube ever since the revelations of the NSA's spying program.
Wretched Hive: Raleigh. Bit-part bad guys hail from there more often than not, and it is often used as the foil to Mayberry's wholesomeness. Nonetheless, the show is as beloved in Raleigh as it is anywhere else in North Carolina.