Is there any issues with reading a newspaper on Shabbat? Assuming you are not carrying the paper into the house without an eruv, I seem to remember hearing that you can not read a Saturday newspaper on Shabbat, but you could read the Friday paper or even parts of the Sunday paper that get delivered with the Saturday paper.
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There may be the issue of shtarei hedyotos - that you're not supposed to read secular material on Shabbos (see Shulchan Aruch, Orach Chaim 307:12ff).
The primary issue most often cited is Nolad* - 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).
**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.
This is talking about a religious newspaper.