I think Salinas v. Texas is the oddest case of the term, from SCOTUSblog:
"The question before the Court in this case was whether this protection of silence applies before a suspect is actually arrested. The defendant in this case, Genevevo Salinas, voluntarily went to the police station, where officers interviewed him about a pair of 1992 murders. When asked whether a shotgun given to police by his father would match shell casings found at the crime scene, Salinas did not answer. At his trial for the murders, prosecutors used Salinas’s silence as evidence of his guilt; Salinas was convicted and sentenced to twenty years in prison."
"The Court’s decision was fractured. Justice Alito wrote for a plurality of the Justices (himself, Chief Justice Roberts, and Justice Kennedy), setting forth the rule that the right to remain silent must be expressly invoked. Justices Thomas (joined by Justice Scalia) concurred only in the result, arguing that even if Salinas had invoked his right to remain silent, he still would have lost because the prosecutor’s comments regarding his silence did not compel him to give self-incriminating testimony. These five votes, together, added up to a loss for Salinas, and the rule in Justice Alito’s opinion is the controlling rule going forward. Justice Breyer, joined by the remaining three Justices, dissented, arguing that a defendant need not expressly invoke the privilege against self-incrimination."
More details here.