Military logistics has been deficient in Iraq, and the entire region, for some very practical reasons. First of all, it's expensive. Even with all that oil money, no one wants to spend a lot of cash on providing logistics capabilities needed for troops in combat that might never come. Historically, nations in the region saw their armed forces as more of an internal security force. If invaded, the army could just grab whatever they needed from the civilian economy. Another important angle was preventing the troops from joining a rebellion. Only a few units had access to lots of ammo and fuel, and these were the most loyal troops, who were thus in a better position to defend the government from rebellious soldiers.
The two times Saddam used the military to invade neighbors, these logistical deficiencies were very obvious. In 1980, when he invaded Iran, his troops were only supplied sufficiently, and just barely, to take the oil rich areas just across the border. Iraqi troops failed in this, partly because of logistical shortcomings. The 1990 invasion of Kuwait was successful, but witnesses noted that the invading Iraqi troops promptly began living off the Kuwaitis, because there was no logistical support from Iraq. When the coalition attacked into Kuwait in 1991, they found the defending Iraqi troops poorly supplied and demoralized because of it.
While there are plenty of Iraqis with military experience, there are few of them with any knowledge, or experience, in military logistics. Coalition trainers had to start from scratch to build a modern logistical system for the Iraqi security forces. In the meantime, coalition logistical organizations are keeping the Iraqis supplied, as best they can. Even with the coalition help, there are few capable logistical troops with the operational units, to receive, store and disperse the supplies.
And then there's corruption. Another reason for Middle Eastern nations to avoid investing in logistics, a service which includes stockpiling supplies for military operations, is the likelihood that the stockpiles will be plundered. This stuff is all-too-easily stolen, and there are surviving records explaining how this was done in the Middle East thousands of years ago. Rulers in this part of the world have learned their lesson, and have another reason to avoid investing in logistics.
But Iraq is still at war with Saddam's supporters, and Islamic terrorists. Those 277,000 security personnel need food, fuel, ammo, medical supplies, batteries and much more, if they are to stay in action. The government is going to have to deal with the corruption problem (and it is still very much a problem) if they are ever going to have peace.
Related to the logistics is administrative and medical support. Getting the troops paid on time, and accurately, is still a problem. The lack of a nationwide banking system means many troops get up to a week off a month, so they can take their pay back to their families. The corruption problem (which even Saddam had to struggle with) means making sure commanders don't steal all or part of their troops pay, or create phantom soldiers and grab more money.
While recruiting and training competent troops, NCOs and leaders has been a major chore, building an effective logistics system, in the face of endemic corruption, may prove to be an even more difficult task.
Although Iraq has 277,600 security personnel (army, police and security guards) on duty, it still has major problems keeping them supplied. This is not a new problem for Iraq, or Middle Eastern armies in general. Creating an efficient logistics and administrative system for the Iraqi armed forces is proving to be the most difficult task the coalition has had to face while creating new armed forces for Iraq.