Here are some details about the execution. I thought that it was interesting that an argument broke out amongst the witnesses. Not too much unity in this government but that can be expected in a diverse nation like this:

Saddam Hussein struggled briefly after American military guards handed him over to Iraqi executioners. But as his final moments approached, he grew calm. He clutched a Quran as he was led to the gallows, and in one final moment of defiance, refused to have a hood pulled over his head before facing the same fate he was accused of inflicting on countless thousands during a quarter-century of ruthless power.
A man whose testimony helped lead to Saddam’s conviction and execution before sunrise said he was shown the body because “everybody wanted to make sure that he was really executed.”
[…]
A witness, Iraqi Judge Munir Haddad, said that one of the executioners told Hussein that the former dictator had destroyed Iraq, which sparked an argument that was joined by several government officials in the room.
As a noose was tightened around Hussein’s neck, one of the executioners yelled “long live Muqtada al-Sadr,” Haddad said, referring to the powerful anti-American Shiite religious leader.
Hussein, a Sunni, mockingly uttered one last phrase before he died: “Muqtada al-Sadr,” according to Haddad’s account.
[…]
Al-Rubaie said that while the execution was carried out with due respect to Hussein — and following “all international and Islamic standards” — some witnesses and the executioner could not resist celebrating by dancing around the body after the hanging.
[…]
“It was an Iraqi operation from A to Z,” he said. “The Americans were not present during the hour of the execution. They weren’t even in the building.”
He added that “there were no Shiite or Sunni clerics present, only the witnesses and those who carried out the actual execution were present.”

Read the rest here and see videos of the noose being put on (I would recommend that the executioners not wear those clothes again) and Iraqis celebrating the news of his death.