Jeremy protects the Gutenberg Bible from burning not out of faith (he's a Hollywood Atheist), but because it was the first printed book in Western history.
Jeremy: It represents the dawn of the Age of Reason. You can laugh, but if Western civilization is finished, I'm gonna save at least one little piece of it.
Of course, they were surrounded by literally millions of books, so it was a mite unnecessary sacrifice.
One geologist verbally serving the Vice President after Jack has recommended abandoning the northern half of the United States and moving everyone else farther south. The VP dismisses it all as fake, saying it's 'easy' for him since he's safe up here, before:
Geologist: (bluntly) His son is in Manhattan. I just thought you should know that before you start questioning his motives.
One of the people in the library is dying from an infected leg. Several of the others brave the cold and board an abandoned Russian ship to scavenge medicine for her.