The most immediate problem is the lack of competent, experienced NCOs (sergeants.) The development of such supervisory troops was a major reason for Western armies becoming the dominant military force on the planet during the last two centuries. You cannot create experienced NCOs in a few years, it takes at least a decade. It may be possible to retrain some of the existing Iraqi NCOs, but even that will take more than a few months.
Arab armies are not known for taking good care of their troops. It's more the case that the troops, and the NCOs, are taken advantage of by their officers (stealing wages, ignoring poor living conditions.) American Special Forces trainers can turn this around quickly by insisting on fair treatment for the troops. But this will require selecting "trainable" Iraqi officers and showing them how it's done.
This may require some motivational speeches from American Lieutenant General John Abizaid, the Arabic speaking son of Lebanese migrants to the United States. Abizaid is second in command at Central Command and noted for a lively, televised, discussion with hostile Arab journalists, in Arabic, in which general Abizaid got the better of the encounter by using some sharp words to describe what was wrong with the Arab world. One can imagine Abizaid speaking (in Arabic) to the Iraqi officers and senior NCOs selected for the new army and asking them if they want to be part of an Arab army that can kick some serious ass. And if they are, are they willing to change their customs and habits in order to make it happen. That cadre of several thousand Iraqis would probably say yes to both questions.
But the proof would be in the performance. With responsible and competent (in their military skills) NCOs, you can train the troops up to Western standards. But this demands of the NCOs, and particularly the officers, new attitudes. Arab officers are not noted for spending a lot of time and effort ensuring that their soldiers are eating well, living in decent barracks and have all the equipment they are supposed to have. When officers do that sort of thing, the troops respond enthusiastically to what they are called on to do. Western style training is arduous. It involves days in the field with little or no sleep. It requires troops to learn new skills quickly, and take responsibility for their actions. It means the troops have to look out for each other.
All this has been passed on by Special Forces supervising the training of elite infantry units in foreign countries. But this does not make for a "kick ass army." For that you need an army full of officers at every level who know what they are doing and trust all other officers to know their jobs as well. This is usually not the case in Arab armies, although many Arab officers are aware that in Western armies things are done differently. Many of the Special Forces trainers speak Arabic, so they can explain to the officers and NCOs how it works in the American army, and argue with their trainees about whether it can work with Arabs. Those arguments are part of the training, because it is not common for Arab military men to argue with superiors or instructors.
Which brings us to some serious cultural differences. Arab armies rarely get the kind of constructive competition you see in Western armies. That is because, for Arab soldiers, it is seen as safer to not compete, so no one is "disgraced" by losing, than it is to compete and improve everyone's skills. Of course there is competition in Arab society, in business as well as sports. But the concept of "losing gracefully" is not as readily accepted as it is in the West. This can be overcome. Arab officers attending American military schools over the last half century learned to live with the competition, even if it is a bit of a shock at first. But there will be some resistance to introducing these "barbarian" customs on the entire Iraqi army. No doubt general Abizaid will have to give his "Do you want to be part of a kick ass army" speech many times to keep things moving along.
The competition means officers, NCOs and troops will be expected to take the initiative. This has traditionally been discouraged. Initiative can lead to failure, or unexpected situations. Arabs prefer to avoid both. The new Iraqi army will have to learn to live with it.
In addition to general Abizaids speeches, the Iraqis will also be inspired by two (1991 and 2003) humiliating defeats at the hands of the Americans. Older Iraqis remember the equally swift defeat by the British in 1941, and all Iraqis wince at the memory of being subjugated for centuries by a handful of Turkish soldiers. If change is truly in the air in Iraq, it could result in the first world class Arab army. This development would, if nothing else, give American and the West another reason to pay close attention to Iraq on a regular basis.
In Iraq, the coalition has dissolved the Iraqi armed forces and announced that a new force will be built, from scratch. The United States is one of the few nations that has troops trained, equipped and experienced at this. The U.S. Army Special Forces have, for over half a century, been retraining and rebuilding foreign armies. This includes a number of Arab armies. The Special Forces troops are exceptional in that respect. But what they face in Iraq is a unique situation, because they will be trying to build an Arab army that will not be hobbled by the shortcomings that have crippled the effectiveness of Arab armed forces for the last few centuries.