The t shirt and cape Melvin has, has the Big O logo featured in the Matt Helm movies.
A borrowed plot device from season two, Tony and Roger break into the Bellows's house to get Jeannie and her bottle back. This was used in One of Our Bottles Is Missing (1967).
Tony tells Melvin a bedtime story. Jeannie wants to tell him "Ali Baba and the 38 Thieves" (38 not 40: "I was there", she says), but Melvin says his favorite is "Aladdin and his Magic Lamp". Jeannie says she was there too, and the genie's name was Punjab... her Uncle Punjab.