Andie. Some people hate her for being a Hypocrite who believes in Black-and-White Morality, yet has no problem working with Surly and defends him even when he's being an asshole and only caring about himself, not the park. Others like her for being a Nice Girl, an Action Girl, and for being one of the few characters in the whole movie who isn't a Jerkass.
Surly. Many viewers hate him for his It's All About Me demeanor and for being a dick to everyone including Buddy, his best and only friend. Others sympathize with him and see him as a Jerkass Woobie who gets hated by everyone even when he's trying to atone for destroying the park's entire food supply.
Big-Lipped Alligator Moment: Out of nowhere, the movie stops so that Surly and Buddy can start dancing to Gangnam Style.
Critic-Proof: Was a box office success despite highly negative critical reviews. Also generated a sequel and has a television series in development.
After his head injury and emotional meltdown, Grayson becomes... very attached to Surly. Jumping into his arms, clinging to him, and even kissing him.
Redline (a male mouse) is also a little too adoring of Grayson, swooning at him along with all the park's females, and what's more, he alone faints from how awesomely handsome Grayson is.
Jerkass Woobie: Surly. It's hard not to feel at least a little sorry for him despite his selfish behavior.
Precious, for being a Motor Mouth idiot who tends to annoy everyone around her.
Grayson, for being a very obnoxious, very vociferous, very hammy Idiot Hero. While most of his behavior happened post head injury, before the injury, he was a Narcissist who couldn't stop flirting with Andie.
Too Bleak, Stopped Caring: Almost all of the characters are mean-spirited Jerkasses, Idiot Heroes who believe anything and everythingRaccoon tells them, annoying characters whose relevance to the plot is questionable at best, or Designated Heroes who are only using Surly for their own personal gain, despite the fact they kicked him out the park and don't intend to bring him back even though he's willingly helping them. Buddy is really the only character who isn't annoying, evil, idiotic, or just plain mean to others.
Ugly Cute: Buddy is a rather scraggly looking rat, but his helpfulness and charming personality certainly make him a lot more likable than all the other characters.
Unintentional Period Piece: The Nut Job dated itself right out of the gate by using "Gangnam Style" (complete with an animated Psy in the credits!) nearly two years after the song's heyday (the movie came out in January 2014).
Unintentionally Sympathetic: The film sets up Surly as having to learn to not be such a jerk. But considering almost everyone is a jerk to him for being a non-conformist and that he was banished for a catastrophe which was just as much their fault as it was his, his attitude can be quite understandable.
Viewer Gender Confusion: Precious the pug is sometimes assumed to be a male dog due to Maya Rudolph putting on a pretty androgynous voice for the character.
The Woobie: Buddy. When he isn't acting like a comic relief, he could really use a hug considering how horribly Surly treats him and how he bends over backwards to please him.
