Clear messages about believing in yourself, pursuing your dreams, being brave, trying hard, working together, and performing for the joy of it -- but it's important not to overlook the fact that Buster lies to everyone and still comes out OK/is rescued in the end (though you can also interpret events as conveying the idea that lying to others doesn't succeed and cheaters get found out). Some viewers may also raise an eyebrow at what Rosita's story says about how the movie views motherhood/homemaking.
Mob-like Russian bears want to kill Mike for cheating at cards; a glass aquarium shatters, flooding and destroying the theater in a spectacular collapse (it's not clear everyone is OK immediately, but they are); car chases/pursuits. Police pursue an escaped convict with helicopters and more. Buster puts himself in peril to hook up electricity (illegally). A character is injured when stagelights fall on him. Ash's quills pepper the audience during her song. Some arguments/confrontations.
Mouse Mike sees a female mouse, ogles/flirts with her, and they become a couple after he starts flashing his cash around. A male pig kisses his wife after she sings and dances to "Shake It Off" (wearing what, for her, is a quite revealing/sexy costume). A young, unmarried porcupine couple lives together until she catches her boyfriend cheating on her -- flirting, hugging, and singing with another porcupine. A rabbit act auditions to the lyrics "oh my gosh, look at her butt," waggling their own rear ends. Another act performs a snippet of "Butterfly," which has the lyric "come, my lady." Buster and Eddie wash cars in their Speedo swimsuits.
Insults and exclamations, like "stupid," "fool," "loser," "porky," "nobody," "namby pamby," "fat," "jerk," "holy moley," and "fart." Possible use of "hell" in Ash's song.
Nothing in the movie, but plenty of tie-in merchandise/promotions -- from apparel and toys to accessories, figurines, and Happy Meals.