Integrity, perseverance, and teamwork are important themes. Strong message about identity -- finding your true self, what you're best at, and what you love. Po is told by Shifu: "If you only do what you can do, you will never be more than you are now." And you should be and embrace who you are, not who someone else is. Also, family is more than biology; it's accepted that Po has two dads. While violence remains the main means of conflict resolution, the pandas fight the bad guy with a coordinated effort that involves lobbing food (and themselves!) more than weaponry.
Lots of martial arts fighting, both in groups and one on one. Villain Kai, an angry supernatural bull monster, is intense and scary, as are his jade warriors. Sad flashbacks to Po's separation from his mother when he was a cub. Key characters are captured/in danger. Po makes a big sacrifice that could upset some kids. Additional creative fighting via the use of Chinese food -- spring rolls, dumplings, etc. -- as well as nun-chucks and other means of attack. Perilous trek to panda village. Slapstick falls/crashes.
Mei-Mei is very flirtatious with Po and others, though nothing comes of it.
Infrequent use of words including "stupid," "butt," "loser," "idiot," and "shut it." Some bathroom humor.
No product placement within the film, but plenty of offline merchandise tie-ins, including toys, games, books, and more.