New York City Ballet’s 100th season is underway. “How Balanchine is performed is the central issue at City Ballet, and for years now the record has been worse than spotty. Last season, things were looking up—when they weren’t looking grim. Gala night perfectly symbolized both the ups and the downs. Some of the self-congratulation was justified—there were times when the spirit of Mr. B did come through—but there was trouble, too; Bugaku, one of Balanchine’s most singular ballets, which has been lingering on the endangered-species list, may actually now be extinct.”