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!."
A big part of one arc involves Jeannie not knowing what her actual birthday is because she's lived for so long. Before things really hit the fan, Tony sticks a candle in a glazed donut on his desk and lights it. Then he says "Jeannie? Happy birthday, no matter when it is." Even in this desperate moment, Jeannie looks genuinely touched and blows out the candle.
In one of the Hawaiian-set episodes, Jeannie brings back King Kamehameha. The king is disappointed by 20th century life and thinks that his people have forgotten him. To prove him wrong, Jeannie shows him the Kamehameha day parade, assuring him that his work was not for nothing and that his people still remember him fondly.
A small one: in one episode Jeannie has her powers removed for a week so that she can prove herself to be just as good a housekeeper as Mrs. Bellows. Needless to say, it doesn't go well, and she ends up destroying Tony's dinner and many of his clothes. Nevertheless, instead of being angry with her, he comes home the next day with a gift and a dozen roses to make her feel better (she's not there by that time, but the gesture was certainly sweet).
Even though it caused more trouble, Mrs. Bellows helping Jeannie out of what she assumed to be a bad situation is heartwarming in itself.