In the Pesukei D'zimra of Shabbat, why are the Shabbat-specific portions added before most of the every-day portions? Shouldn't they be said after according to the rule: Tadir V'she'eino Tadir, Tadir Kodem (when there's a common requirement and a rare requirement, the common requirement comes first)?
The purpose and structure of Pesukei D'Zimra is outlined in Shulchan Aruch, but the basic idea is that it all leads up to Ashrei, and specifically the Posuk פותח את ידך. The things that come after that have a specific purpose (finishing until the end of tehillim, and so on - but mainly about providing praise to Hashem and the types of praises, leading up to Yishtabach which expresses that concept).
So in terms of the structure of Pesukei D'Zimra, some of the things that we add on Shabbos are additional meditations intended to be before Ashrei (broadly - about Hashem's creation and control of the world), whereas what is added afterwards (before Yishtabach) is about the idea of praising Hashem. So within their respective sections of Pesukei D'Zimra, they are at the end, following the principle of Tadir Vshe'eino Tadir, Tadir Kodem.