The taunting of Saddam did not help the cause. Everything "hangs" (ugh) on the new government establishing itself as a real, legitimate authority capable of performing basic functions effectively. Executing their former head of state should have been a solemn occassion of great gravity, performed efficiently and without glee, in a maner that preserves the dignity of the state and the condemned.
From a practical standpoint, Saddam still has a lot of fans. To the degree his execution looks like the work of a Shia vengeance mob, these folks are antagonized for no good purpose.
The accidental decapitation is a similar screw-up. To the average Joe: "If the government can't even get a hanging right, how are they going to keep the electricty coming to my house?"
There's an argument to be made that executing these guys was not a good idea anyway, that the government's interests would have been advanced by having a clean break with the past: "This government doesn't kill its citizens." I don't think it is a convincing argument, since Saddam's continued existence and the interminable trials would have been an ongoing distraction from important business.
