The state education commissioner, Richard P. Mills, has appointed a new superintendent, Robert-Wayne Harris, for the troubled Roosevelt school system in Nassau County. Mr. Harris, whose three-year term starts on Oct. 15, has been an assistant superintendent in the neighboring Freeport school district for the past five years. In 2002, after decades of mismanagement and weak student performance, Roosevelt became the only district in New York to be placed under state control. But problems have continued, and the 2,800-student district now faces an $8 million debt and could run short of cash for daily operations by next month unless the State Legislature moves to authorize a bailout.