From what I can see, the problem isn't whether or not they have a Constitution. In fact, the Constitution of Afghanistan appears to outline fundamental human rights and freedoms, and shares many, many values as those outlined in our constitution.
So why are all these issues still present? I believe it comes down to the application of their constitution, and the efficiency of the government's power. Like it or not, the Taliban and similar forces still have a strong hold on how things work in Afghanistan, and the Constitution can only do so much when such powerful forces see no need to abide by it.
Discrimination, lack of justice, and overall corruption of basic human rights and freedoms (especially for women) were all prominent issues in Thunder Over Kandahar, and these issues are also seen again and again in the news and in other media and publications. These issues are going on, and yet the Constitution of Afghanistan says these shouldn't be present. Words in a document are only of so much value. The key is to have a government that supports and enforces their constitution, and a nation without powerful forces working against it.
In Afghanistan, the innocent are just as much victims as those who do bad. Not only are they not safe, they are prosecuted.
Let's take a second and compare with Canada's charter. If Afghanistan had the Canadian Charter of Rights and Freedoms, it probably wouldn't make a difference. It might even make things worse. Why? Our Charter reflects the western worldview and our values, not that of Afghanistan. Gender equality, life, liberty: these are very western values. And in our Charter, they are expressed in a very western way. Furthermore, Afghanistan has a decent Constitution, outlining rights, freedoms, and other guidelines to a democratic society. It's just not actually applied. So if Canada's Charter was applied in Afghanistan, we might actually see these issues being resolved.
Somehow, I don't think that's going to happen any time soon...