Break the Cutie: Jim gets hit with this hard. He goes from being a genuinely upbeat, cute kid to a brooding teenager because of the way his father abandoned him. There's also the fact that he regularly has trouble with the law, isn't doing very well in school, wants to make his mom proud...
Brilliant, but Lazy: He's pretty good at building things and figuring out mechanical stuff, but at the start of the film he only uses that to amuse himself.
Celibate Hero: He doesn't has any romantic interest during the entire movie.
Character Development: Jim goes from the moody, sullen, rule-breaking Emo Teen, who only uses his smarts for his own amusement to a military cadet who is more happy and smiling, and learns not to be so angsty.
Crouching Moron, Hidden Badass: Jim is a lot smarter and pragmatic than most give him credit for. Over the course of the movie, he learns to curb his impulsive tendencies and think more logically.
The first is after the supernova incident, when Jim is convinced that he was the one who murdered Mr. Arrow, he barks at Silver about how badly he screwed up. It's one of the more beautiful scenes in the movie, and marks a character shift for Jim.
The second is when he learns Silver was actually a treacherous pirate all along - he tries his damnedest not to cry and then as Silver leaves the room to check out the threshold of Treasure Planet, Jim quietly stumbles around the room with a heartbroken, shocked expression on his face.
Sensitive Guy and Manly Man: The Manly Man to B.E.N.'s and Doppler's Sensitive Guy. Although, he's only really a "manly man" in comparison to those two. In general, he's actually quite vulnerable, probably even more so than them.
Also the Sensitive Guy to Silver's Manly Man.
The Stoic: Hardly shows any emotion, except the usual teenage angst. He starts to change over time.
Break the Cutie: A rare adult version, but let's look at what she had to go through: Her troubles with raising Jim, the Inn burning down to the ground, and a flashback shows her weeping when Jim's father leaving his family. Seeing this woman so broken is heartwrenching. She got better though.
Broken Bird: A flashback of Jim's showed his mother just breaking down in tears after his father left them. Combine that scene with what happened in the beginning and you'll know she qualifies.
Glamorous Single Mother: Averted. She is not a single mother by choice (her husband just left straight up left her, for God's sake) and she struggles with her restaurant to get by. Possibly played straight after the climax, though!
He Is Not My Son's Father: She is horrified that the robot guards assume Delbert Doppler is Jim's father, accidentally insulting Delbert quite a bit.
Parents as People: She tries to do her best for Jim, but is overworked and likely still emotionally hurt by his father abandoning them.
'''Doctor Doppler: "Dang it, Jim!I'm a astronomer, not a doctor! I mean, I am a doctor, but I'm not that kind of doctor. I have a doctorate, it's not the same thing. You can't help people with a doctorate. You just sit there and you're useless!"
She Is Not My Girlfriend: Doppler reacts this way when BEN thinks him and Amelia are a couple because he's carrying her. Although, his expression when B.E.N. does mistake them as a couple is otherwise.
Adaptational Heroism: Long John Silver of Treasure Island was very charismatic and managed to make all the heroic characters like him even as they distrusted the rest of the crew, but ultimately he was a murderous pirate who only cared for himself and the treasure. Here, he forms a genuine bond with Jim, as opposed to the empty flattery and lies he feeds him in the book, and ultimately sacrifices what's left of the treasure to save Jim's life.
Adaptation Name Change: He's never referred to as anything other than "Silver", and is never confirmed to have the "Long-John" moniker he had in the original novel.
Affably Evil: Never loses his affable nature, even after revealing himself as the villain.
Anti-Villain: No doubt he's a villain, but no doubt he cares a lot about Jim.
Love Redeems: His paternal love for Jim causes him to give up the treasure he's been searching for possibly his entire life just so the boy will live.
A Man and His Morph: Silver found Morph in one of his adventures and they've been close ever since. Until Silver asks Morph to stay with Jim; a reminder of the close bond between Jim and Silver.
Minored in Asskicking: Though he is the ship's chef, his leg is a damned howitzer and his arm can blow apart doors with a single shot.
Mysterious Past: Jim asks how Silver got the mechanical cyborg limbs of his body, to which Silver replies: "You give up a few things, chasing a dream." The event is never mentioned again, but it's enough to make one wonder... what exactly happened to Silver?
Noble Demon: His morals are loose, but there's no doubt that his concern for Jim is genuine. Especially proven in the climax.
Obfuscating Stupidity: While at first glance he's an affable, outgoing chef, in reality he is a cold and ruthless pirate captain.
Decomposite Character: While he is rather clearly based off of "Israel Hands", a similarly unhinged pirate from the original novel there actually is a different crew member on the ship named "Hands" (though his name is never spoken in the film).
Greed: Flint is so greedy that he would set the entire planet to explode, then let someone take his treasure.
No MacGuffin, No Winner: Apparently, he had this attitude toward his treasure. Rather than allow anyone else to get their hands on it (even with Flint himself long dead), he rigged the entire planet to explode if anyone entered the treasure chamber.