Dog lifespans are discussed as a reason to cherish your dog while you are still together. At first, the dog does not appear in the flash-forward segments, which may lead viewers to conclude that the dog has died in the interim; however, it is eventually revealed that the dog is still alive and fine.
There is discussion of fictional minors being sexualized ("manga artists might be lolicons!") but this is not shown, and the children who are real in-universe are free of sexualization.
Hime is mislead into believing that her father has a different job but it is done for both her safety and comedic effect for the audience that her father needs to upkeep this ruse.
There is a gag about a character being mistaken for a stalker because he is acting like one (standing outside the fence and spying on the child he's supposed to be checking on).
A recurring gag has Kakushi unwittingly lead on three different women who then get upset at him for "dating" the others, but it is made clear that he has no idea of the impression he's giving off and is still holding out for his missing wife.
The flash-forward segments take place in a coastal town and the ocean is shown. Hime's mother also disappeared above the ocean, and many times the manga staff plan to or do go on beach vacations.