Goober's dog is the same dog Barney uses in a previous episode to track down an escape convict, "Barney's Bloodhound."
Opie and Tommy's secret agent game was typical of the times. James Bond and his imitators were peeking in 1965 with films like "Goldfinger" and "Thunderball" being all the rage, leaving western and cops 'n' robber games behind.
When Opie and his friend ask Goober for the number of the man who had a horse for sale, Goober said he didn't have a pencil handy but he had 1 pencil and 4 pens in his front pocket.
According to the calendar in Floyd's Barber Shop, it is February when this episode takes place, 28 days in the month. The outside scenes show lush green leaves, short sleeves, and warm temperatures. It is still very cold in North Carolina in February.
As a subtle Indicator that Tommy is a boy who comes from a more well-to-do family, the wardrobe department has him in slacks and polo shirts, with Opie just wearing common button-downs and jeans.