Ok, here's argument.

> People are wrongfully executed all the time

Citation needed. I'm not aware of people who have been persuasively shown to be innocent post-execution.

> Executions serve no purpose for society except to satisfy our thirst for revenge,

Wrong, many studies show a deterrent effect.

> it makes little difference if the person they kill is innocent or not.

What? Of course it does.

> If he turns out to be innocent, they can always execute someone else to save face. Not the ones responsible for his execution, of course.

This hardly deserves a response.