Capital Punishment, Due Process and the Constitution

Three young children died in a house fire in Corsicana, Texas in 1991. In a two-day trial, their father, Cameron Todd Willingham, was convicted of murdering them by setting the fire. Just before he was scheduled for execution in 2004, an independent investigator reported that the fire was caused by accident, not by arson as Willingham's jury had been told. He was executed anyway. Since then two more investigations have found no evidence of arson. One was commissioned by the State of Texas. Did the state execute an innocent man? If the evidence was faulty, does the Constitution require that his life must be saved, or does his "full and free trial" justify the death penalty anyway?