These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ironically, many foreign dubs (the Italian, the Japanese, and the German dubs) changed Jeannie to be a witch. It is rumored that the dubbers mistook the show for a spin-off (or tried to retcon it into being one).
Crowning Moment of Heartwarming: In "The Moving Finger," Jeannie schemes to become a Hollywood actress in order to impress Tony, who seems to be starting a budding romance with a starlet named Rita Mitchell. At Jeannie's screentest, it is revealed that Jeannie cannot be filmed. Humiliated and cheated, Jeannie breaks down crying, being reminded yet again how she will never be good enough for Tony. Meanwhile, Tony sneaks in and explains he broke his date with Rita to see Jeannie's test. Upon hearing this, Jeannie lights up and says, "I cannot believe it...I have taken thee away from the greatest star in Hollywood!."
Ear Worm: The upbeat theme tune that was used from Season 2 on.
Fair for Its Day: The alternative interpretation to Reactionary Fantasy. Tony explicitly freed Jeannie in the first episode, never took advantage of her Happiness in Slavery and consistently refused to exploit her powers for his own advancement — all fairly enlightened for a man of his era. So was his alleged desire for mundane conformity actually a sign of integrity? One could easily see how a man with enough drive to become an astronaut would not want a walking Deus ex Machina to just hand him the things he was intent on achieving on his own merits.
"Funny Aneurysm" Moment: In "Mrs. Djinn-Djinn", a woman asks Jeannie whether she is pregnant. At the time, Barbara Eden was pregnant with her second child, but complications with it caused it, in short, to end in a miscarriage.
Ho Yay: Tony generally seems more interested in hanging out with his astronaut buddies than giving Jeannie, a pretty blonde in a harem girl costume who is willing to be his literal slave, the time of day. The fact that he has no problem whatsoever with his fiancee, Melissa, leaving him also has shades of this.
Apparently, this was because the writer who developed Serena went to work for I Dream of Jeannie.
Values Dissonance: There was considerable controversy during the episodes where Jeannie's costume showed off her belly button.
Vindicated by Cable: While the show was by no means a flop, and its cancellation was due more to it being the network's plaything than anything, the show did tremendously well in syndication.
Unfortunate Implications: In early episodes, Tony has a fiancée, Melissa, until Jeannie successfully breaks up the match. Jeannie actually broke up a potential marriage out of jealousy and is essentially rewarded for it. To her credit, it is implied Tony was not going to go along with the marriage anyway.
The Woobie: Jeannie. Her tragic backstory consisted of being stripped of her humanity and being trapped in a bottle by a wicked djinn (though she was later retconned to have been born a genie), her mother and sister are outright evil, and Tony could be cruel to her.
Tony's treatment of Jeannie gets lampshaded in "Divorce, Jeannie Style", in which the Bellows meet Jeannie and mistake her for Tony's wife, and nearly bring Tony to the authorities over Domestic Abuse.
Her actress, Barbara Eden, counts as a woobie, too.
Dr. Bellows. How can you not feel sorry for him every now and then? Especially since he and Amanda are very friendly to Jeannie when they finally meet her!