Boisterous Bruiser: Relentlessly cheerful and the only member of the team to seriously consider hand-to-hand combat against some of the (much bigger) villains.
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.
Deadpan Snarker: Not as often as Chip, but he likes to make side comments to Zipper when somebody's being foolish.
Dinner Deformation: An episode has Monterey Jack unwittingly eating a piece of dehydrated cheese. When it rehydrates in his stomach, he's comically stretched out into a large brick shape. .
Leeroy Jenkins: Varies a bit by episode: when 'look before you leap' is supposed to be the lesson of the show, Monty's the bad example.
The Navigator: Unsurprising, considering the number of times he's been around the world, and is shown to be skilled at navigating by the stars.
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).
The Storyteller: Almost everything he encounters reminds him of a previous exploit. Although his memory isn't the best.
Stout Strength: Overweight: Check. Gadget even tries to get him to lose some weight. Strength: Check. He's easily the strongest Ranger.
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).
Super Strength: Courtesy of cartoon physics, he's definitely got more lifting power and leverage than his size suggests.
Team Chef: He's usually the cook. The others have gotten accustomed to a certain... cheese element... in their usual menu.
Team Dad: Has an avuncular fondness for the whole crew, although he's pretty irresponsible for this trope.
Theme Naming: Monty's name, as well as his parents', are taken from cheese. "Cheezer" sort of fits in here, too.
Balloon Belly: In "Out To Launch", the Rangers eat so much aboard the spacecraft that they all show much rounder shapes while relaxing and digesting. This does not exclude Gadget, she looks like she's pregnant.
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.
Dude Magnet: Both Chip and Dale fell in love with her. She's also caught the eye of villain Rat Capone, who keeps urging her to sign up with him.
'80s Hair: Her big hair is certainly a sign of the times in which the cartoon was made.
Lethal Chef: Referenced: Dale tells Foxglove that Gadget's cuisine always tastes like machine oil.
Oblivious to Love: Very much so. Double-O Chipmunk made it obvious that Gadget knows she's attractive (and, at her team's request, uses it as a last resort) but she seems to avoid relationships - she may be shy of losing another loved one. She was pretty obviously attracted to Sparky (from Does Pavlov Ring A Bell?)... but he was even moreOblivious to Love. Fanon has been all over the place with this.
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.
Parental Abandonment: Gewgaw's disappearance is unexplained and her mother is simply never mentioned, but To The Rescue shows that Gadget was effectively orphaned and took it hard.
Science Hero: Hilariously true to the trope. If a solution doesn't exist, make one.
* She Cleans Up Nicely: To carry the role of the classic Femme Fatale in Double O Chipmunk, Gadget switches to a slinky red dress, a blond(er) wig, heels, makeup etc.
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 ceremonial tests that would qualify her to be queen of a Hawaiian tribe.