Aunt Bee tells professor St. John "why don't we have some Elderberry wine. It's Andy's own recipe." Yet another example that Mayberry is no longer a dry county, like in the earlier seasons of the show.
Aunt Bee tells the Professor that she moved in with Andy and Opie in 1959, but in fact Season 1, Episode 1, "The New Housekeeper," originally aired October 3, 1960.
The professor would have explored much more than South America in his career. He jokes with Clara about the relative dangers between a leopard and a pretty girl. There are no leopards in South America.
The professor tells Bee that "Beatrice" means "bringer of joy" in Latin. This is actually a later connotation. "Beat" is Latin for "blessed," as in "beatitude," and "trice" comes from "trix," Latin for x 3. Aunt Bee is "triply blest." Dante used Beatrice in "The Divine Comedy" as a symbol of blessed grace, to be followed through the trials of Heaven and Hell.
Several times during the color era Bee will be sitting in the living room sewing fabric that always turns out to be one of Opie's shirts, which he will either wear later that episode, in the next episode, or in this case the previous episode "Opie's Group," when he visits Emmett's shop to get his amplifier checked out.