The primary issue most often cited is NoladNolad* - that we may not use that which has come into existence on Shabbath, and must treat it as Muktzeh, inasmuch as Muktzeh may not even be handled. For a more traditional example, one may not handle an egg that a chicken lays on Shabbath. Masecheth Beitzah is basically premised on this notion.**
See here for a lengthy discussion on the subject of newspapers with various issues raised, not just Nolad (Hebrew): http://seetorah.com/Shiur303%20RavPearl.pdf*See here for a lengthy discussion on the subject of newspapers with various issues raised, not just Nolad (Hebrew).
**It might be more precise to say that Beitzah, which is about the laws of Yom Tov, is premised on the difference(s) between Y"T and Shabbath and takes as its starting point the case of an egg laid on Y"T and whether or not one may eat it.