I spent yesterday evening reading through the Iraqi Constitution. Not what would call a typical evening read but readable enough. You can download your own copy here, in English, translated from Arabic by Associated Press.
I am here in the danger of burying the lead, so let me begin by noting that constitutions are fairly straightforward documents delineating the "thou shalt" and "thou shalt not" for everyone, and the Iraqi constitution is no different. What is different though about the Iraqi constitution is that instead of it being the "supreme law of the land", as in the United States, it leaves the authority over a variety of actions to "the law", as legislated by the representative council. This substitution leaves open vast tracts of authority and freedoms to the whims and fancies of elected representatives, despite the overarching framework provided for what kind of laws can be promulgated. Their document is full of statements like "No one can be captured, detained, jailed, or searched except in circumstances defined in law" which leave the freedoms granted in the constitution harder to maintain.
Every legislation has to adhere to the following principles - no Law may contradict "the undisputed rules of Islam" or the "principles of democracy" or the "rights and basic freedoms outlined in the constitution." But this is not particularly reassuring given that the body that would adjudge the constitutionality of laws, i.e. the Supreme Court, would follow the laws of Shar'ia in addition to the laws of the land (which very well could be the same).
The rhubarb about the Iraqi constitution is not only over the power vested in the representative council (or parliament if you will), it is also over the kind of elected representatives – especially the first elected council which will have the power to change parts of constitution - that Iraq will choose in an atmosphere heavy with identity politics and religious radicalism.