I've seen a few instances of this famous wordplay, but this time reading the play I decided to look for it specifically. And when I had this "wordplay hunting" as my focus, I found that the play is just loaded with it - especially with Armado and Moth (who you'll remember from my last post about Love's Labour's Lost).
So here are some examples:
Moth: Master, will you win your love with a French brawl?
Don Adriano de Armado: How meanest thou? brawling in French?
Moth: ... and make them men of note—do you note me?
Don Adriano de Armado: How hast thou purchased this experience?
Moth: By my penny of observation.(I think this is like saying "a penny for your thoughts")
Moth: And out of heart, master: all those three I will prove.
Don Adriano de Armado: What wilt thou prove?Moth: A man, if I live; ...
("Prove" as in "I will show you" and "prove" as in "become")
Moth: As swift as lead, sir.
Don Adriano de Armado: The meaning, pretty ingenious? Is not lead a metal heavy, dull, and slow? ...
Moth: You are too swift, sir, to say so: Is that lead slow which is fired from a gun?(Good point.)
Costard: Pray you, which is the head lady?
Princess of France: Thou shalt know her, fellow, by the rest that have no heads.
Costard: Which is the greatest lady, the highest?
Princess of France: The thickest and the tallest.("Head" and "highest" as in "main, principal, chief" and also as in "the body part above the neck" or "height" and "stature")
Biron: ... they have pitched a toil; I am toiling in a pitch...
All this, especially Moth and Armado, made me think of yet another classic comedic gem: