This year, Iraq truly returned to the rule of law. U.S. troops now have to obtain a warrant from a judge before raiding a house. They can't grab just anyone, but have to have reasonable cause for an arrest. These new rules were widely popular in Iraq, because U.S. troops were mostly looking for terrorists, and you have to cast a wide net to catch the bad guys. A lot of innocent people are disrupted, or taken away, during these operations.
But in the months before the new rules went into effect, American soldiers were increasingly going after criminals. By the end of last year, the gangsters were more of a bother, and threat, to civilians than were Islamic terrorists. The common criminals were better known than the terrorists, but harder to get a warrant for. So the Iraqi police liked the fact that the American troops could just go in and round up the usual suspects, without a warrant or the usual probable cause. The gangsters, more so than the terrorists, had lawyers handy, and were better at dealing with the judicial system. But the American raids not only locked up gangsters, but often uncovered evidence of crimes (stolen goods, or kidnapping victims.) Now that's gone, as the U.S. troops can't raid anywhere without building some kind of case first.
While there are still Islamic terrorists at work in Iraq, their attacks have declined by more than 95 percent from the 2007 peak. Criminal activity has declined only slightly, and the police spend most of their time and effort going after the gangs. This causes problems for U.S. troops, who are supposed to have some police along with them when they go to execute a warrant. The police often don't want to be bothered, mainly because they are more preoccupied with catching crooks, and because terrorists are more likely to resist violently. Terrorists, when cornered, will often put on a bomb vest and come right at you. That's not what the cops signed on for. Terrorists often want to die, and the police don't want to be around when that happens. The police appreciate the training they continue to receive from foreign police advisors (largely retired detectives or police commanders), but are no longer as enthusiastic about running with the more direct and violent U.S. troops.
Iraq has many special, often quite good, counter-terror units. But these guys prefer to operate on their own, and not just go along on American raids to show the flag. So U.S. troops get the impression that Iraqi police just don't care about taking down the dwindling number of terrorists. That's not quite true. The police are simply more concerned with the more frequent depredations of the common criminals, and so is the average Iraqi.