Brainwashed and Crazy: Whenever he smells cheese, he goes into a trance and (sometimes) causes a path of destruction in his wake. The local police precinct recognize him from the many times he's stolen cheese slices off their sandwiches and burgers, cheese hunks from the mouse traps, and even a bag of cheese-flavored popcorn.
The Navigator: Unsurprising, considering the number of times he's been around the world, and is shown to be skilled at stellar navigation.
Noodle Incident: Monty only half-remembers the adventures he's been on, and there was an incident involving cheesebread and Gadget's father, Geegaw, that led to a friendship dissolution. Then there's the matter of Monty's cheese attacks — how exactly did Monty come to have them if it's not genetic (both his mom and dad have been shown in the series and there were no signs of either Cheddarhead Charlie and Camembert Kate having them).
Strong Family Resemblance: He does look a lot like his father Cheddarhead Charlie (who coincidentally was voiced by Jim Cummings. "Parental Discretion Retired," the episode that introduced Cheddarhead Charlie, was one of the episodes that had Peter Cullen as Monterey Jack).
Ditzy Genius: She can make almost everything from almost anything, including rebuilding a plane out of garbage, but she simply does not register that in certain circumstances, certain behaviors are socially necessary or unusual.
Maybe she just isn't interested in chipmunks. She was pretty obviously attracted to Sparky. (Unfortunately for her, he was even more Oblivious to Love.)
Furthermore, Gadget is aware of how attractive she is and is willing to use it to her advantage in the absence of any other option at the request of her team.
Only One Name: Yes, Gadget has a last name, but after the Five-Episode Pilot it's never used again, and even then it was only used when naming her father, Geegaw Hackwrench; meaning Gadget's last name being Hackwrench is really only a logical assumption.
No Matter How Much I Beg: Lahwhinie knew Gadget would try to escape when the dangerous challenges started, so she tells Shaka Baka that she's scared and might chicken out, but wants him to make sure she goes through with it.
Spell My Name with an S: Apparently Its All There In The Manual somewhere (said manual being extremely hard to come by), but no one is 100% sure just how her name is really supposed to be spelled. The Writer's Bible spells it "Lahwhinie", the DVD subtitles spell it "Lawhinie" which is just how most people spell it, and some closed-captions during TV airings spell it "Louwhiney". That's three practically official sources which contradict each other.
The german synchro actually managed to give her a new name that is just as unspellable.
Twin Switch: She tricks Gadget into switching places with her so she wouldn't have to be put through the cerimonial tests that would qualify her to be queen of a Hawaiian tribe.