1.11. Two brothers are involved in a murder. Though it's clear that one of them actually committed the crime, neither can be punished. (This is different from #1.78.) (from "Unreasonable Doubt," by Stanley Ellin)
1.11 answer: One of the brothers (A) confesses to the murder. At his trial, his brother (B) is called as the only defense witness; B immediately confesses, in graphic detail, to having committed the crime. The defense lawyer refuses to have the trial stopped, and A is acquitted under the "reasonable doubt" clause. Immediately afterward, B goes on trial for the murder; A is called as the only defense witness and he confesses. B is declared innocent; and though everyone knows that one of them did it, how can they tell who? Further, neither can be convicted of perjury until it's decided which of them did it... I don't know if that would actually work under the US legal system, but someone else who heard the story said that his father was on the jury for a very similar case in New York some years ago. Mark Brader points out that the brothers might be convicted of conspiracy to commit perjury or to obstruct justice, or something of that kind.
1.11 variant answer: Scott Purdy says an L.A. Law episode had a similar plot: A petty criminal and a mob boss were accused of murdering someone. The lawyers offered to drop the charges on the criminal if he'd testify against the boss. He said he would, got his charges dropped, and confessed on the stand. Both got away without being punished: the charges couldn't be reinstated for the one, and there was reasonable doubt for the other.