Intelligence collected from messages sent by remaining pro-Saddam commanders indicates that Saddam is either dead, or hiding from his own people as well as coalition troops.
Looting and crime in Baghdad is slowing down as many neighborhoods, groups of merchants and large families bring out weapons and guard their neighborhoods, shopping districts and family compounds. Nurses have been seen standing guard at hospitals with rifles or pistols. Attempts to get Iraqi policemen, and other civil servants, to return to work have been hobbled by the inability of the coalition troops to assure the Iraqi workers that they will get paid. Arabs, in general, don't volunteer to work for nothing, unless it's a family or clan matter. Some senior Iraqi civil servants have come out of the woodwork, but some of these, according to Iraqis who are working with coalition troops (translators and medical personnel, for the most part) have recognized some of these senior bureaucrats as people who have long been known for their corruption and greed. But American Civil Affairs troops are pouring into Baghdad and, neighborhood by neighborhood, are trying to calm things down and get the government going again. Combat units are increasingly running heavily armed patrols through the most troublesome areas. Intense fighting breaks out when they run into Iraqis who still want to fight. But most Iraqis now realize that you can't defeat American combat troops, and only with a bit of luck can you even wound or kill any of them. This is discouraging a lot of young Iraqis from joining the fight.
Britain is starting to withdraw some of it's forces, mainly warplanes and warships no longer needed. British troops in Basra continue to provide useful lessons on how to pacify a large Iraqi city. The British got into Basra over a week before Baghdad fell, and have been using tried and true pacification tactics as well as improvising as needed. American troops elsewhere in Iraq are benefiting from this experience.
Mosul, a largely Sunni city in northern Iraq, fell without a fight. But armed resistance remains. As the major Sunni city in the largely Kurdish north, Mosul has always been more pro-Saddam than most Iraqi cities. Looting has broken out, and it is felt that irregular armed resistance may last a bit longer here.
U.S. troops are approaching Tikrit, the last major city still held by pro-Saddam forces. There is thought to be one brigade of the Republican Guard there, as well as thousands of pro-Saddam men with weapons. But the city has been heavily bombed and continues to be watched 24/7 from the air, and bombed daily.
U.S. Special Forces examined an oil pipeline from Iraq to Syria and discovered it was still in use. So they used explosives to destroy it. The working pipeline was evidence of Syria breaking the UN sanctions by illegally importing Iraqi oil. This apparently accounts for the Syrian support (denied by the Syrian government) for Saddam during the coalition invasion.
In the Arab world, a widely believed reason for the rapid fall of Saddam Husseins government is that Saddam was bribed to quickly lose. These delusional attitudes are common in the Arab world, as are a number of other bad habits that limit their military effectiveness, and their ability to run effective governments. Too many Arabs will not trust anyone outside their family. This is an ancient curse that many European cultures only overcame in the last few centuries. But it's still a major problem in Arab lands, meaning that Arabs in the same region or nation are reluctant to work together with their neighbors. Another major problem is the tendency to avoid personal responsibility. Some say this is an Islamic thing. After all, the word "Islam" means "submission" and a popular attitude is that anything happens because "God wills it." Millions of Arabs who agree with neither of these precepts have migrated to Western nations in the last century, where they have done quite well. But too many of the folks who stayed behind are mired in a culture of selfishness and lack of personal responsibility. These attitudes will be run into a lot as the coalition tries to rebuild Iraq.