The appearance of Shia death squads, from within Iraqi special police units, was not particularly surprising to those who have been training the Iraqi police for the last two years. Priority has been on developing competence (at defeating terrorists) and loyalty (to the government). When recruiting, these requirements left out most of the available Iraqi counter-terrorism experts. That's because these fellows had worked for Saddam Hussein, were reluctant to go after fellow Sunni Arabs, and didn't believe the Shia and Kurd dominated government was legitimate. So new police commanders had to be created from scratch. While that worked for junior commanders, the senior guys had to come from a different pool of talent. That is, leaders of Shia and Kurdish militias. These fellows had experience supervising large numbers of armed men, and fighting terrorists (either Saddam's secret police or Islamic radicals). The downside was that these newly minted police commanders really, really had it in for Sunni Arabs. Not just the ones who terrorized Kurds and Shia Arabs while working for Saddam, but Sunni Arabs in general. Despite admonitions that many of the new police commanders might start going after Sunni Arabs, with minimal cause, and maximum violence, the government was more concerned with stopping terrorist attacks. In a sense, you can say that this worked. Those Shia and Kurd dominated police units that went over to the dark side, did indeed terrify a great many Sunni Arabs. This was just what al Qaeda wanted, but it did not create the desired civil war (which was to cause enough general chaos for al Qaeda to take over, or at least that was the plan.)
Instead, the terrified Sunni Arab population asked the government for protection, and offered up the Sunni Arab terrorists (al Qaeda and otherwise.) This led to the collapse of the Sunni Arab terrorist effort. Now, the government believes it can safely shut down the rogue police units. That won't be easy, but not impossible either. But many of those death squad cops are heroes to the majority of Iraqis (the Shia Arabs and Kurds who suffered three decades of Saddam's death squads.)
What most Iraqis want now, are not death squads, but cops who can keep the streets safe. So the new training effort will not only screen out the death squad types, but try to create a police force that can take out the hundreds of criminal gangs that terrify the average Iraqi more than al Qaeda does. In some respects, the gangs are more formidable than the Islamic terrorists. Although not as bloody minded as the terrorists, there are more criminals out there, and they directly confront (and often kill) more Iraqis. The gangs instill more fear than the terrorists. Remember, the terrorists would only go after you if you did something they did not like (work for the government, or foreigners, or sold booze, videos and so on.) The terrorist bombings could be largely avoided as well (stay away from police stations, government businesses and so on.) But the gangsters came to you if you had anything worth stealing. They would rob you, extort you (often via a kidnapping) and keep after you day and night.
The police will have a harder time with the gangsters than they did with the Islamic terrorists, and the politicians are already feeling the heat over the issue. Saddam could afford to ignore a lot of criminal activity back in the day, but the current elected politicians cannot.