This is the 125th of 249 episodes, meaning that this is the halfway point of the show's original eight seasons. There were 124 episodes before and 124 episodes afterward.
Gomer tells Thelma Lou that Barney works for the city. In fact, Barney is a Deputy Sheriff. The Sheriff's Office is a county, not city, agency.
Barney has a conversation with Andy about "that doctor show on TV" that he and Thelma Lou watch every week, describing the star as a "young doctor." In 1964, he would've been talking about "Ben Casey" or "Dr. Kildare."
In this episode, Barney tells Andy that Mount Pilot is 12 miles from Mayberry.
This is the only episode with Thelma Lou's name in the title.