What challenges remain for the Iraqi government now that American troops are gone?
The challenges are significant, and actually, rather daunting. There is no doubt that the situation in Iraq is far better than it was in 2007, one of the worst years in the war for attacks on US troops and sectarian warfare, but there is still plenty of potential for the nation state America has helped to build and protect to fail.
America's nearly nine year presence in the country could not hope to quell centuries of Sunni vs. Shia rivalry. Iraq was always an artificial country, held together by the military might of the British Empire and then by military dictatorship after independence. Besides Sunni and Shia, there is also a Kurdish minority in the north that is already autonomous and would love to be independent, something nearby turkey has said they will not allow. Shia and Sunni militias effected a sort of cease fire around the time of the Sunni Awakenings, when they both combined to fight al-Qaeda.
With al-Qaeda largely gone, and American troops too, the old Sunni-Shia tension could escalate. Iraq's parliament could come apart along religious and sectarian lines. Corruption could taint the credibility of the new government with their citizens (in some ways this has laready happened). Neighboring Iran, a Shia state, could work to influence elections, ship weapons, or otherwise undermine the existing government.
Clearly a number of challenges remain, but Iraq's oil wealth could make for a smoother transition. Whether Iraq becomes something like a democracy or anything like stable remains to be seen.