Motivation: Loius Pojman mentions in What Can We Know? (2001) of a certain Carneades (ca. 214-129 B.C>) who must have been a "remarkable dialectician"because " in 155BC he was sent on a diplomatic mission to Rome and in his spare time he gave two lectures. On first day he eulogized justice, making a profound impression on his audience. To their amazement on the second day he gave a diatribe against justice, arguing that there were equally good reasons for not adopting it".
Research yielded the Carneades argumentation framework. However I am interested in the more recent ones. Here's one:
The Mathematical Proof that got a Physicist out of a Traffic Ticket
Dmitri Krioukov, a UC San Diego physicist, was recently given a ticket for running a stop sign. He went to court to argue the ticket, armed with a scientific paper that mathematically demonstrated that he really had stopped. He won.
Krioukov has since posted the entire paper, rather immodestly called "The Proof of Innocence", on the arXiv server. It's probably debatable how much his ironclad mathematical reasoning really helped determine his innocence - it's just as likely the judge threw out the ticket when it was demonstrated another car had obstructed the ticketing police officer's view. Still, let's take a look at...
Are there any similar cases?
EDIT: Peter Suber has a description of the case on the famous Paradox of Court here.