Bunny-Ears Lawyer: Jessie is arguably the goofiest of them all, but is crazy-skilled, including singing, stripping a gun, survival training, hand-to-hand combat skills and being able to fly aircraft. It was also revealed in the pilot that she's a straight-A student. It's implied her dad is just as ditzy and skilled.
Forgotten Anniversary: She initially thought that Tony had forgotten their one-year anniversary, but she was the one who actually had the date wrong.
Flanderization: The writers seem to have become stuck on her having bad relationships with guys and as Season 1 progressed she seemed more and more like a relationship chaser (possibly a Disneyfied Good Bad Girl or Ethical Slut) than a girl with just enough bad experiences to make her play it safe with Tony. As many relationship stories as she's mentioned, it seems like she dated every single guy in her hometown at least once. The stories are becoming more outlandish as well.
Also the whole Failure Is the Only Option angle. Jessie started the show being able to fly helicopters and bragging about winning talent shows; in Season 2 she comes off as being lucky if she manages walk down the hallway without being run over.
Improbable Piloting Skills: Jessie is capable of flying a helicopter, as evidenced by the pilot. In a later episode, "We Are So Grounded", she crash-lands a jet in an emergency. She calmly prefaces her aerial antics with "my father taught me how to fly!"
The Fashionista: Peyton R. List, a Real Lifefashionista, mentioned in an interview that Emma's original wardrobe prior to her being hired was cute but somewhat normal compared to Peyton herself. As a result the wardrobe people used Peyton's own style to help make Emma more of a true fashionista. They sometimes collaborate Peyton's clothes with the wardrobe choices for Emma to create even more outfits.
Screw the Rules, I Have Money!: Though not to the same extent of Big Bad Mrs. Chesterfield, Emma acts this way from time to time and more than the others, especially in the crossover episode. In fact, if she wasn't rich and pretty, it would've just been super creepy for Austin and friends to stay the night, not to mention dangerous. But since the Ross family is rich, they all but begged to stay in the penthouse.
Spoiled Sweet: Emma is a classic example as she could easily be an Alpha Bitch, but has proved on numerous occasions that she is far from being one. She is still spoiled and pampered nonetheless.
Techno Wizard: She's pretty tech savvy, being able to repair a broken apart cell phone or airplane radio, which are fairly complicated devices that need to be assembled by precise machines or very skilled technicians.
Token White: Among her siblings (even if excluding Luke is a stretch).