Grenades lie unattended next to a west Mosul bazaar. Garbage bags throughout the city are searched daily for bombs. At a sprawling sheep market, Iraqi army soldiers are careful not to kick over rocks for fear of setting off hidden explosives. War has ebbed in most parts of Iraq, but not in Mosul, the third-largest city and Al Qaeda's last stronghold in the fragile new democracy. And time is running out on the around-the-clock U.S. military patrols of Mosul. U.S. troops must vacate cities by June 30 under an agreement with the Iraqis, and President Obama is ending all American...