Magic Skirt: Averted. One episode that calls for Emmy to do cartwheels has her wearing overalls.
Not So Above It All: Since Emmy is usually portrayed as the responsible sibling who, in Max's words, can "do anything", it's intentionally portrayed as rather jarring during the rare occasions when Emmy acts irresponsibly (such as the time she broke Wheezie's trumpet and then lied about it) or demonstrates weakness (when jerks tease Emmy's team during a basketball game, Emmy's the one who takes it the hardest and thus, she's the one who learns the episode's aesop about not letting teasing bother you).
Pride: Emmy's biggest flaw, but given the non-hostile nature of this show, it really only comes up a few times, such as Emmy being unable to cope with losing a game, or wanting Max to do things her way which summons a literal "Copy Cat".
Spirited Competitor: In "Tails, You Lose," she didn't want to play if she couldn't win. At least at first.
Dragon Rider: He gets Zak & Wheezie, much to their delight, because as a general rule they usually had nobody to ride them before, unless either Max & Emmy were feuding with Ord or Cassie respectively.
Super Strength / Stout Strength: He can throw a baseball so hard that it goes out of bounds in seconds. While it is never revealed what happens when it lands, it could be implied that it can cause massive structural damage.
Innocent Prodigy: She's very talented in multiple ways (for example, according to Zak, everyone knows she does "the best cartwheels in Dragon Land"). However, since she's a child, she gets upset sometimes and usually cries when she gets upset.
Nice Girl: To such a huge extent that one episode makes a point of this being her talent, i.e. "being a good helper". If the topic of Cassie comes up in a song, it'll usually be about how sweet she is.
Afraid of the Doctor: In one episode, which becomes a problem when he needs a doctor to remove a rather large thorn from his foot. Apparently he fears the doctor because he thinks it'll hurt; he even pre-emptively reacts before the doctor even touches the thorn. So the doctor makes him grab his sister's hand and squeeze, so he doesn't even notice the thorn being removed until after it's out.
Neat Freak: To his credit, though, this is usually played as a virtue instead of a vice, except in one episode where the color in Dragonland disappears, and he approves of the change since it makes everything so neat and clean.
Stealth Mentor: Quetzal is easily capable of solving many of the problems that come up in the episodes, but instead he uses those problems as a way to guide the young ones into learning lessons on their own.