In this episode, Opie decides he'll study to be a dentist while his friend, Arnold, has decided to be a doctor. Sheldon Collins, who played Arnold in many episodes (but did not actually appear in this one), is in reality now a dentist.
Andy asks Helen if a state college like University of North Carolina at Chapel Hill would be affordable. UNC was Andy Griffith's alma mater.
This episode marks the first time in the series that a courthouse window is seen being open. While Opie is sitting on the bench outside of the courthouse, the window behind him is open as he listens in on Andy's conversation. The only other time a courthouse window is open is in "A Girl for Goober."
In this episode, Opie is intent on becoming a dentist. But in the 1986 reunion special "Return to Mayberry," it is revealed that Opie actually winds up as a newspaper writer/journalist. Ron Howard's other famous character, 'Richie Cunningham' (from "Happy Days") also winds up as a journalist/screenwriter. And in real life, Ron Howard did indeed write a number of screenplays (in addition to being a successful actor and director).
Andy's laundromat uses the same storefront as Mrs. Luken's lingerie shop in "The Bed Jacket" from Season 3. It was just around the corner from the Mayberry movie theater, and across the street from the building front used for Dr. Peterson's office in "A New Doctor in Town."