Iraqi government forces must prove to the people of Mosul that they are rebuilding an inclusive Iraq. This message is vital to any immediate military success, and to rebuild any civil administration for the city and the surrounding provinces where Daesh (the self-proclaimed Islamic State of Iraq and the Levant) has held untrammelled sway for two and a half years. This is why the report of gross abuse of civilians by uniformed Iraqi personnel is deeply troubling, whether they are in the regular army or in one of the government-sponsored militias.
Now that the government has recaptured east Mosul, its forces are taking control and are naturally looking for Daesh sympathisers and sleepers who have remained behind to cause future mayhem. If it is to be successful for the long-term political stability of Iraq, this task has to be conducted with some decorum and active participation of legal authority. It is both a crime and a political disaster for Iraqi uniformed personnel to encourage the clubbing of civilians and their shooting to death on the spot, to describe only one of videos circulating on social media at present.
If the inhabitants of Mosul see themselves as about to be liberated, they will covertly help the Iraqis and maybe actively hinder Daesh. But if rumours and social media encourage them to think they are about to swap one occupation for another they will simply hide in their homes and pray that the violence will wash over them, and they will quietly opt out of rebuilding their state. Which would be a tragedy.