The National Security Agency has at times mistakenly intercepted the private email messages and phone calls of Americans who had no link to terrorism, requiring Justice Department officials to report the errors to a secret national security court and destroy the data, according to two former U.S. intelligence officials. At least some of the phone calls and emails were pulled from among the hundreds of millions stored by telecommunications companies as part of an NSA surveillance program. James Clapper, the director of national intelligence, Thursday night publicly acknowledged what he called “a sensitive intelligence collection program” after its existence was...