The Los Angeles County Board of Supervisors has launched an investigation into the failures that allowed problem employees from Martin Luther King Jr.-Harbor Medical Center to continue working in violation of county policies. Acting Auditor-Controller Wendy L. Watanabe was ordered to complete within four weeks an investigation that will identify those responsible for the flawed oversight of the problem employees and to recommend reform. But the supervisors acknowledged that any reforms that improve the tracking of employees would not necessarily be in place before the county moves forward on a long-delayed downsizing of hospital staff in August.