This search slip shows the destroyed file—"HQ 9-57023"—and several others that Cronkite's name shows up in, according to the FBI's filing system. One of them—"NY 145-3591"—appears to have been an obscenity investigation.

This page appears to show the search results in the FBI's system for the destroyed file, indicating that it was created in January of 1974 and also involved two unnamed individuals.

This says 9-57023 was "DESTROYED" in October 2007.

This is the FBI's numerical code for different varieties of crimes—the number in the left-hand column begins each file number for investigations into the corresponding crime.