Uggabugga diagrams the Pickering issue.
They key points on the cross burning trial are that Pickering approved a plea bargain that two out of the 3 defendants agreed to. He later was upset that the third defendant, who decided to go to trial, got a longer sentence than the "ringleader," despite the fact that the potability for receiving a higher sentence at trial is one of the foundations of the plea bargaining system. He was additionally upset that the juvenile "ringleader" was getting a smaller sentence because he supposedly subsequently (after the plea bargain) found out that the defendant had previously fired a gun into the house of the couple in question even though this information is present in the trial transcript during the defendant's plea. And, while you would think this would just make him regret his decision to accept the plea of a low sentence, he instead decided to somewhat inappropriately pursue a lower sentence for the third defendant.