As Iraqi soldiers and police take over most the combat operations in Iraq, American units are still struggling to upgrade the quality of Iraqi forces. It's not just training and mentoring, corruption is still the main problem. In Sunni Arab areas of central Iraq, the police are recruited locally, and are still vulnerable to bribes or threats from terrorists or criminals. Throughout Iraq, the major source of corruption is the criminal gangs (some of which carry out terrorist operations on the side.) Taking a bribe is an ancient (we're talking thousands of years) tradition in the area. Family ties also count for a lot. If you are a criminal and your cousin is a cop, you have a useful resource inside the police department. If money or kinship doesnt work, threats will. If making the threat doesn't have the desired effect, kidnapping a family member will often work. This risks kicking off a family feud, but if you are really into the criminal life, this is not a major issue.
Another big issue is the rather more laid back attitude of the Iraqis. Unless there's an imminent danger, the Iraqis will move at a leisurely pace, if at all. They view the Americans as a bunch of hyperactive workaholics. There are exceptions. An energetic Iraqi commander can make a big difference, but even these officers know that it is not wise to push their subordinates too much. Such commanders are rare. Partly because most officers are of recent vintage. Before 2003, Sunni Arabs, especially Sunni Arabs loyal to Saddam, monopolized most leadership positions in the military and police. Some of these officers have been allowed to come back. But most of them have been permanently replaced by Kurds and Shia Arabs who are still learning how to command army and police units. The Sunni Arabs had another advantage in that their ancestors had been in charge for centuries. The Kurds and Shia Arabs are still getting used to all this responsibility.
The situation is made somewhat worse by the policy of taking many of the more energetic and entrepreneurial Iraqis and putting them in elite army and police units. This produced some outstanding outfits, but deprived the majority of units of some very good leadership. Most American units don't get to work with the elite Iraqi SWAT teams, police battalions and army commandos, and find the regular units to be a very mixed bag. The consensus is that it is going to take 5-10 more years to train many of the officers and NCOs to an acceptable standard. Until then, a lot of army and police units are going to be of questionable effectiveness. That is, the army units will not be very effective in a war, and the police units will be very corrupt and inefficient. For most Iraqis, that just déjà vu, but it also makes the country more vulnerable to internal disorder, and foreign invasion.