The Bellow's house is the same house/set used in Bewitched for Samantha and Darrin's house but is simply redressed.
Jeannie's bottle is a painted and gilded bottle of Jim Beam's Choice bourbon. On her official Facebook page, Barbara Eden has stated that she still has this bottle.
Not only is the exterior and interior set the same as the Stephens's home on Bewitched, the painting in the entranceway is Soyer's "Dancers at Rest," which hung over the fireplace in the Stephens's master bedroom during the early seasons of Bewitched.
The closing credits music is a different arrangement, unique to this episode only.