Characteristic of Shakespeare, since Much Ado About Nothing is a comedy, a vast amount of puns, or play on words, can be found all throughout the play. Listed below are a few:
The first pun can actually be found in the title. The word "nothing" is a pun because the Elizabethan audience would have heard it as "noting." The Elizabethans considered "noting" to be another word for observing, or even eavesdropping, and as we see, the consequences of eavesdropping is a central theme in the play. Hence, the title is a pun that can also be translated as Much Ado About "Eavesdropping" (Chidester, "Much Ado About 'Noting'").
Another pun can be found in the opening scene when Beatrice refers to Benedick as "Signior Mountanto" (I.i.25). Mountanto can be interpreted as referring to "montanto," which is a fencing term referring to an upward thrust. Hence, this is a play on words being used to refer to Benedick's poor fencing skills.
A third pun can also be found in this scene. Beatrice refers to Benedick as a "very valiant trencherman" (42). The word "trencherman" can refer to a person with a big appetite and Beatrice is arguing that the only reason why Benedick joined the company in the wars is because he was given free food, or "musty victual," meaning "stale food" (41). However, trencherman can also mean parasite, showing us that Beatrice is making a play on words to portray Benedick as both a person with a big appetite and one who takes advantage of others, such as taking advantage of free food.
"Claudio: Now you talk of a sheet of paper, I remember a pretty jest your daughter told us of.
Leonato: O, when she had writ it and was reading it over, she found Benedick and Beatrice between the sheet.
The word sheet is used to refer to a piece of paper and used to refer to a bed sheet, with an innuendo placed in between about Beatrice and Benedick.
Beatrice about Claudio: "..civil as an orange" to describe his jealously and bitterness (Seville orange is bitter and yellowish in colour)
The title itself is a major pun "Much ado about nothing" nothing meaning zero, zilch. It also was a slang in Shakespearean times for female genitalia.
Hope this helps ^^