I believe I am in a position to comment on this topic since I returned from Iraq in Dec of 2011 and one of the missions my unit was tasked with was advise, train, and assist to the IA.
A little background first. I participated in the invasion of Iraq back in 2003 and the fiasco that occured in the year following the fall of Baghdad. My unit set up the first ICDC training facility in Al Anbar province outside the city of Al Hit. We trained the ICDC for about 2 months and it was...frustrating. Lack of understanding of culture, different training methods, lack of funding, dubious motivations for joining the Iraqi military, wasta, etc plagued our efforts to train these first recruits in the ways of the warrior.
Fast forward to 2011, the Iraqi Army I encountered was much better than the one I encountered in 2003. BUT, there were still several shortfalls. I can only speak of the IA that I worked with and trained with...I can in no way validate or invalidate the respective quality of IA forces outside of my area...
When I arrived in Iraq this last deployment I was a platoon leader inheriting the battle space that was previously the responsibility of an entire US Infantry Stryker Company. My platoon consisted of myself and 18 soldiers responsible for the entire 46 IA Bde that was located around the volitile area of Hawijah and Riyadh. The 46th had a very experienced officer corps, most officers of the rank of Maj and higher had previously served as officers in Saddams Army. Many of the officers, NCO's, and soldiers were Kurd. A very few were Shi'a and the rest (probably about 60%) were Sunni Arab.
They had a good grasp on the basics of soldiering but they were plagued with bad supply and aging equipment. My Brigade was equipped with M16 rifles(the only brigade in this division equipped with them, the others being equipped with the AK47) but lacked adequate training in the operation and maintenance of them. In addition, they did not have enough 5.56 ammunition to go around. I would regularly spare any extra ammunition, medical supplies, chemlights, and extra equipment to help these guys out...needless to say, it was the proverbial finger in the dam scenerio. We did many raids with the IA and in my experience they were eager to do the job, but, they lacked the necessary patience and planning expertise to be truly effective. Many times when conducting a joint op, they would go off to the objective without waiting for the order, only to not find anything because we could not set up an effective cordon in unison with the raid...the targets would slip through the unsecured portion of the cordon in the fiasco that followed.
They had only one mortar platoon for the entire brigade but no ammunition to shoot it. they had zero armor, almost all of their transport being up armored humvees and ford/toyota pick ups with machine gun mounts on the back(a technical). They were often spread quite thin and some of the soldiers within their ranks(officers included) were sympathic to one VEN group or another.
Their NCO corps is weak and the officer corps kind of fills this gap. We tried to empower the NCO corps while we were there but it is hard to do because we are dealing with some cultural barriers on how to run a military.
Now the good news. Their intelligence apparatus is excellent. They have their fingers in everything and seemed to be privy to a lot of the FVEY info I read on our daily GRINTSUM. Their source network was mind boggling. Once I gained their respect they went out of their way to keep me informed of any SIGACTS in my AO and their soldiers WILL fight. They have no lack of bravery under the right circumstances. They're not a 100% solution by American standards, but they are a 70-80% solution by their standards and that distinction is important. A 100% American solution will not work. They will simply defer to our help and throw their hands up. A 70-80% Iraqi solution is far more important because they can see that they can do it. They have a very complex honor system over there. US soldiers demeaning Iraqi performance in front of others is the biggest dishonor we could do. Instead, by allowing them to do it their way, with our help, they save face and are genuinely grateful.
They are a military that CAN provide stability within Iraq over time. They are well versed in COIN and have a very experienced and battle hardened corps of soldiers that stay and fight for the good of Iraq. Unfortunately, they are not a combined arms military. This was a big gripe that many of the Field Grade Officers I dealt with had. They felt they should not be fighting in the cities dealing with the internal threat but be focused on the external threats like Iran, Syria, Turkey, etc. They don't have the capability to repel an invasion of any significant size and they know it...But, deals are being made and they are slowly starting to purchase modern air, armor, and artillery. Furthermore they are sending many of their soldiers in these highly technincal fields to military schools within the US to get a trained group of soldiers in their ranks so they can set up their own technical schools. It's going to take time, and it's not going to be easy...but I believe in 20-30 years the fruits of our, and more importantly their, labors will spring to life and they will really be a force to be reckoned with within their region.