WASHINGTON—Seated behind the bench for oral argument, the justices of the Supreme Court train their robust intellects on America’s most vexing legal questions.

Unless they’re passing notes like bored teenagers.

“Harry. Stay awake,” Justice Antonin Scalia wrote to Justice Harry Blackmun during the final argument of the 1990-91 term, on whether the Federal Insecticide, Fungicide and Rodenticide Act allowed town supervisors to restrict aerial spraying over a rural Wisconsin tree farm. (It did.)

During a December 1974 argument, Justice William O. Douglas proved himself a judge of fashion as well as law. “We should not give this guy many points in his argument,” he scribbled about an unidentified lawyer at the lectern. “But as far as his jacket is concerned, he comes out way above the average.”

Such writings form a small, if illuminating, subset of some 15,000 handwritten documents that Timothy Johnson, a political-science professor at the University of Minnesota, has copied over two decades from archives housing the papers of former justices. The passed notes provide “an interesting insight into what they were thinking about as the attorneys were arguing,” Mr. Johnson says. “They talked about sports, they talked about selling their houses.”