Bee and Clara recall their days when they met at Sweet Briar Normal School. This would've been around 1920; probably the women's college in Virginia with that name.
Apparently Andy has a next door neighbor named Tillie Kincaid that's really nosy. She lives on the other side of Andy's fenced in backyard.
Throughout the series it's indicated that Bee has no formal or post-secondary education, but normal schools in the 20th century were teacher colleges.
Richard Collier plays Mr. Simmons. He will appear twice more in the series, as another Mr. Simmons in "The Statue," and in Season 8 as Mr. Giddings, the auto-laundromat salesman in "Andy's Investment."
Floyd's cultivation of pansies is a sly invention of the writers to reinforce the idea that Floyd is a delicate man, referencing the slang term "pansy" for weak and ineffectual men. The ancient Greeks believed that pansies could be used for powerful love potions, and are referred to several times in Shakespearean plays as "Love-in-Idleness", with their ability to rob men of their normal motivations.