"Lest We Forget", about the reunion of two lost lovers is one whole episode of heartwarming.
"Don't Say Goodbye": A friend of the real Amy Crane took over Amy's identity after she had passed away, rather than tell her long-lost grandmother Agatha the truth, and had helped take care of Agatha ever since.
Amy: It's not Amy, Agatha. I'm Carol. Carol Foster.
Agatha: Oh, dear.
Amy: And I am not your granddaughter.
Agatha: Well, perhaps not of my blood, but you are my granddaughter.
Amy:(sobbing) Why didn't you say anything?
Agatha: Because all my life I dreamed about having a granddaughter.
Every time Higgins expresses (and attempts to hide) his concern and fondness for Magnum. "Aw, Higgins, you were worried about me." "Nonsense!"
Higgins' interactions with Zeus and Apollo are likewise revealing. He cares for the lads as if they were the children he never had.
"Rembrandt's Girl": Despite being trapped in a bank vault for the better part of a weekend, Magnum and Susan finding they have a lot in common and eventually adorably falling asleep together definitely counts. The great chemistry (and, at the end, unique laughs) of Tom Selleck and Carol Burnett is at least partly why.
Once he is finally reunited with his daughter Lily in "Resolutions", Magnum happily takes on the role of proud, doting dad pretty much immediately.