Adventure Time is a cheerful yet complex world -- its inhabitants care about each other and usually treat each other with respect and kindness, but they frequently have complicated emotional and social problems best understood by tweens and up. They're sweet, though: Before the Ice King relates a terrible story, he takes time to kiss his friends goodnight.
Cartoonish and comic violence/grossness includes an attack by a giant s'more, Princess Bubblegum vomiting a stream of pink candy, characters knocking into each other and slapping each other in the face. Finn always carries a sword and draws it in the face of danger but only uses it infrequently and then only to poke at creatures or knock them down.
Very subtle references to sex, like when Finn tells Jake he likes getting "late-night bedtime calls" when his friend is "sleeping over at Lady's." One of the subplots of this miniseries is romantic, so there's talk of dates, what to wear on dates, how one acts when they have a girlfriend, and the like.
No cursing, but there's questionable and sometimes hurtful language: "heck, yeah," "sucks," "dang," Jake calls Finn a "worry baby" and Fern a "weirdo."