Pretty much the entire film, really. There's so much random nonsense, silly punning and sheer bizzareness that it borders on Rapid-Fire Comedy.
Ringo: I could have sworn it was a yellow submarine! But that isn't logical now, is it? It must have been one of them "unidentified flying cupcakes" — or a figment of me imagination... <beat> But I don't have an imagination.
The defeated Chief and Max:
Chief: It's no longer a blue world, Max. Where could we go? Max: Argentina?
Anything with the Chief Meanie is a trifecta of horror, Funny Moments, and Crazy Awesome, especially if you can't understand what's he's saying.
"You're advancing the wrong way! Retreat backwards!"
The scene when George tries to fix the motor.
George: Let me peruse 'er — [accidentally electrocutes himself] John: Well, what do you think? George: I think I burnt me finger...