I've seen a lot of news reports about how women's rights may be threatened by incorporating Islamic law into the Iraqi Constitution, with no specifics on why that's the case. Bad journalism - what else is new.
Juan Cole has published some specifics. Unfortunately, I can't find the link for his discussion of child custody under Shiite sharia law, but hopefully my memory is accurate. Upon divorce, the husband's family automatically gets custody of the couple's children. So the only way a woman could get rid of an abusive or otherwise awful husband is by losing her children, who will then be unprotected from the tender mercies of that husband, his family, and his other wives. I call that a recipe for enslavement of women, or disaster for their children. Ironically, this somewhat parallels Saddam Hussein's biography as a child - he was semi-abandoned by his mother, mistreated and generally unloved.
I did find another Cole posting with some other specifics:
"Jaafari's system will give girls half the amount of inheritance that their brothers receive, and may well make women's testimony worth half that of a man in court. If strict gender segregation is enforced, and coeducation ended, Iraqi women may find it difficult to get post-BA training, since they won't be allowed in the professional schools (now coded as "male"), and mostly won't have professional schools for women, or in any case many fewer than for men."