St. Louis County prosecutors last week took steps to vacate the murder conviction of a man on Missouri’s death row. The move followed a review of the decades-old case that left prosecutors doubting the conviction. Across the state, the Jackson County Prosecutor’s Office operates a conviction integrity unit tasked with performing similar work. But local attorneys and advocates say the unit, or CIU, has failed to take seriously its mission to correct wrongs in the criminal justice system. The unit does not follow several recommendations made by national experts: It does not have written policies…