While the Iraqi National Army has been improving steadily, efforts to professionalize Ministry of the Interior paramilitary security forces, notably the police commandos, have not been as successful. Some elite police units are very corrupt and frequently have ties to local tribal and criminal networks, and even links to Sunni Arab groups fighting the government. Reportedly a police brigade in a large city in the central part of the country has been pulled out for "retraining" and "reorganization."
This sort of corruption is nothing new in Iraq, or the Arab world in general. The usual solution is to have several different secret police organizations, who keep an eye on the elite police units, and publicly execute those caught misbehaving. Without some kind of restraints, Iraqi cops are going to do what Iraqi cops have always done; misbehave.
Coalition trainers have been trying to convince police commanders that the future of the country depends on honest and effective police. This appeal has often succeeded, but not always. The government is reluctant to crack down, since the cops, both honest and corrupt, tend to close ranks when "attacked" by the government. What the government can do is "retrain" police units, and quietly remove the most corrupt commanders. That might work.