Islam will be "a source," not "the source," of law. However, there is other language "prohibiting the passage of any legislation 'against' Islam." How will all that play out for the rights of non-Muslims and women?
Here's a full report from the New York Times.
That's the open door for Sharia. Without that clause, Iraq has a chance. With it, a snowball's chance in hell.
Sharia and reason are mutually exclusive. If religion and state are not kept apart in Iraq, making belief the personal choice of the individual and not a policy enforced by government, Iraqis will have lost, never knowing what was in their grasp.