Everyone Died. The End.

Explain why the ending of the play proves that it is a comedy, and give specific examples from the play. What would have had to happen instead were this play a tragedy?

Much Ado About Nothing is a comedy, mostly because it ends on a happy note, but there are other reasons for it. For one, it ends with a celebration, a wedding, and the villain is punished, or about to be dealt with. 

In Act 6, Scene 4, Lines 115-17, Benedick says: "Come, come, we are friends. Let's have a dance ere we are married, that we may lighten our own hearts and our wives' heels." This shows that they were getting married and there was a celebration. 

A few lines later, 123-24, a Messenger comes in and tells Don Pedro: "My lord, your brother John is ta'en in flight, And brought with armèd men back to Messina." Benedick responds with: "Think not on him till tomorrow. I'll devise thee brave punishments for him" (5.4.125-26). This demonstrates that the villain is about to be dealt with. 

For Much Ado About Nothing to be a tragedy, someone/everyone would have had to have died. Hero would have died instead of fainting at the wedding, and then Benedick would have killed Claudio for Beatrice and ended up dying in the process, and then Beatrice would have killed herself because of Hero and Benedick. Leonardo would have probably have killed himself too, because of Hero and Beatrice, and then Don Pedro and Don John would have battled each other and both end up dying, leaving only the unimportant characters alive.