The new Iraqi police force has proven difficult to create. It's been pretty much built from scratch, and largely outside the country at that. There's not a lot to build on. Under Saddam, the cops were constantly overruled, and often abused, by Saddam's secret police and paramilitary militias. As a result, the old police force was not very effective. There were exceptions. Some policemen and detectives took a lot of really bad people off the streets. But Saddam's thugs were mainly interested in people who disagreed with Saddam, and would even work with criminal gangs to this end.
Many of the old Saddam era cops were brought back in 2003, which proved a mixed blessing. Many were corrupt, and made up rules as they went along. These old timers needed more training than the new recruits, because they had to unlearn bad habits, before they could absorb more effective procedures.
The most effective training has been conducted in neighboring Jordan. There, the International Police Training Center uses Arabic speaking instructors (from Jordan, and other Arab countries) teach modern policing methods. There are also instructors from Western nations. Giving police this much quality training is an innovation for the Iraqis, who were taught decades old techniques because Saddam saw no point investing money in his neighborhood police.
The Jordanian center conducts several different courses, in addition to Police Work 101. There is a training course on IEDs (which the Iraqis are getting hit with more than the Americans these days), and another on how to defend a police station against hostile attack. Back in 2004, it too common for terrorists and Sunni Arab gangs to attack police stations, kill all the cops and loot the place. That rarely happens any more.
The basic police training includes modern investigation methods (which, previously, Iraqis only saw on American TV police shows) and procedures that protect suspects from abuse. In Iraq, there's still the attitude that you're guilty until proven innocent. The instruction also covers the downside of corruption. However, in Iraq, many people take it as an insult if a cop doesn't accept a bribe. Dealing with corruption is going to be a long term project.