Did the Shinsekai Yori anime cover all of the material in the light novel? Did the Shinsekai Yori anime cover all of the material in the light novel?

Is there more content past episode 25, and would there be more content to continue the series?
There's no content "past episode 25", per se - the novel1 ends just where the anime does, with Saki putting Squealer out of his misery, and finishing with a mention of the sign in the academy that reads 「想像力こそが、すべてを変える」 ("Imagination can change everything"). As such, there isn't any content on which one could base a sequel. 

However, it isn't quite the case that the anime covered all the material in the novel - clocking in at around 950 pages of dense prose2, the novel contained many bits and pieces that didn't make it into the anime. 

Some of this is probably because of restrictions on the kinds of content that can be shown on TV - e.g. somewhere around what would be episode 8, Saki witnesses Satoru and Shun having sex, and this is described in the novel in great detail (though not in a salacious way). 

Most omissions, though, were probably just because of constraints on the amount of time available to the anime - Shinsekai Yori is an incredibly detail-rich story, and translating all that detail to the screen would require far more than just 25 episodes of anime. Remember how we got nearly a full episode of infodump from the false minoshiro in episode 4? That's the cut-down-for-TV version of that scene. In the novel, the false minoshiro speaks for around twice as long. 



1 Do note that Shinsekai Yori is an actual novel, not a light novel.

2 In the one-volume edition, anyway.