In Fallujah, most of the remaining hostile gunmen have been forced into a small section of the city. Other gunmen are still operating in areas already fought over. This is a common situation in this kind of fighting, especially with a foe that often uses suicidal tactics. American troops encountered this a lot while fighting the Japanese in the Pacific, particularly when fighting in towns and cities of the Philippines. The situation is different, of course, in Iraq. The Iraqi fighters are poorly trained compared to the World War II Japanese, and much more poorly equipped. American night vision equipment and UAVs provide a tremendous edge, which is why some 25 Iraqi gunmen die for each American death. Very few civilians have been encountered in Fallujah. Those that claim to be civilians are given a "residue test" to see if their hands have fired a gun or handled explosives recently. Very few young men in Fallujah come away clean.
Up north in Mosul, the Sunni Arabs in the city are trying to drive out the Kurds, just as Saddam had done for several decades. The largely Sunni police often refused to oppose the Sunni Arab gunmen. More armed Kurds, and American troops, are headed for Mosul. With the Sunni Arab gangs of Mosul now out in the open, they can more easily be destroyed.
Al Qaeda leader, Abu Musab al Zarqawi, who long operated from Fallujah, released a statement condemning Shias and Kurds for supporting the "American invaders." Zarqawi had long supported the idea of getting a civil war going in Iraq, which would somehow make it easier for al Qaeda to take over. It hasn't worked out that way, with the Sunni Arab resistance being a lot less than Zarqawi expected. Now Fallujah is lost and Sunni Arab gunmen are unable to take control in any other cities. The Sunni Arab violence just makes more Shia, Kurds and even Sunnis, support the new government.