Now that Kosovo's new constitution has been adopted by parliament we start seeing comments about how it was made. I found an interesting article on Lifesitenews (an anti-abortion site). Some quotes:
President Fatmir Sedjiu told the group that he had “trusted the experts” that Kosovo was compelled to include sexual orientation so that Kosovo would have a “contemporary” understanding of international human rights. Jakup Krasniqi, president of Kosovo’s assembly, said that he had opposed the article but that UN, European Union, and Council of Europe representatives told him that the reference put Kosovo’s law in line with other European constitutions.
Kosovars criticized the fact that they were not allowed to see the draft Constitution though they were encouraged over the past year to offer “public comment.” They also objected to the fact that all of their comments to the constitutional commission, the small body of experts responsible for the drafting process, apparently needed review by the representative from an American NGO called the International Research & Exchanges Board (IREX) during the proceedings.
Kosovo’s religious leaders said the constitutional commission never sent them a copy of the draft document. After consenting to meet Catholic and Muslim leaders, the commission agreed to omit language that would have explicitly removed legal protection from the unborn, but never provided promised feedback on other complaints and instead claimed “consensus” had been reached.
Another discontent community are the Turks. There language will not become an official language. A bit painful as Turkey was one of the first countries to recognize Kosovo. But Roma and Bosnian aren't becoming official languages either. It would become much too expensive.
It doesn't sound like the content of the constitution has much local support.
Addition on 20-6-2008: For another critical artical about Kosovo's constitution see here. This article takes a libertarian US viewpoint.