Gadget acting drunk after someone drugs his drink in "A Race To The Finish," to the point where he starts doing donuts on the racetrack.
Gadget's horrifically bad attempt at flying a rickety airplane in "Photo Safari," starting with this exchange:
Penny: Are you sure about this Uncle Gadget?
Gadget: No problem, Penny! The nice mechanic said any fool could fly this plane!
And fly it he does. Upside down, sideways, through buildings and nearly into the ground, all before leaving the runway area. What really makes it hilarious it is Penny and Brain's shell shocked reactions, though - while Gadget's whistling and singing, completely oblivious to the danger they were just in as usual, Brain's freaking out and Penny frozen to her seat looking like she's having trouble not joining him.
The episode "Quiz Master" has a funny bit where a M.A.D. agent disguised as a bearded caveman in a stovepipe hat tries to waste Gadget, only for the bumbling detective to avoid the attack and say "Sorry, Mr. President".
This exchange from "Gadget's Clean Sweep".
Dr. Claw: "You must get the Crown Jewels. I wanted them since I was a child."
Thelma Botkin: "You were a child?"
In a movie filled with groaners, when Gadget is battling the evil Robo-Gadget, he's hanging over the edge, holding on by his tie:
Robo-Gadget: Hey Gadget — it's a clip-on!
"Somebody's been watching too many Saturday morning cartoons!"
And how can we possibly forget the part of Inspector Gadget's training session where his guru tells him to focus completely upon "obtaining the balls." More specifically, a pair of balls on the floor in front of him. Gadget's cybernetic hand extends as desired...and then it keeps going, rocketing straight at another pair of balls...
[The Guru screams like a little girl; cut to the observation room, where the onlookers wince in sympathy] Guru: (In the highest-pitched voice imaginable) Ungrip! Ungrip! Turn it off! TURN IT OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOFFFFFFFFF!!!!!!! Chief Quimby: Well, I guess six million dollars doesn't buy what it used to. Brenda: Excuse me. [As hospital workers put the guru in an ambulance, with an ice pack on his crotch] Guru: (Still in the highest-pitched voice imaginable) He is not a man, you know. Oh! He is a monster! (Sobs in pain)