The title refers to a go-go that was a dance club for young adults in the 1960's.
First time Barbara Eden didn't wear a veil to conceal her pregnancy and following the birth of her son Matthew.
The car driven by Roger that Jeannie crashes into is a 1965 Mercury Comet. This is unusual because Pontiac provided cars for use (and promotion) for the main characters and even some guest stars throughout the 5-year run of the series. They were always convertibles, except for Dr. Bellows who drove a variety of Pontiac sedans and wagons ("Safari").
It was common (and still is) for a landscape painting to replace sky, yard, street, etc outside a window or door on a TV sound stage set. As Jeannie opens the door to go out on her date with Roger, a house with a tall tree behind it and other to the side are the landscape painting. Reality is that the real "I Dream Of Jeannie" House has a park out front. Literally, the "Friends" fountain in the opening credits is walking distance from the house and in that mini park. It is the same park where Tony will be dragged by two dogs. Also, it's the same park Samantha Stephens takes Tabitha on Bewitched.