Character mistake: The Fifth Amendment Double Jeopardy Clause does not apply. Libby could be convicted of 1st Degree murder when she gets out and pursues Nick. It doesn't really matter to the plot, however, because it was what Libby believed to be true and motivated her. Further, she ends up shooting Nick in self-defense. So it's all good.
Character mistake: When Tommy Lee Jones is attacked by one of the other women in the halfway house as she's being arrested, he calls her "Libby."
Suggested correction: Jones actually says "Ruby" several times during their skirmish. I watched this scene on Netflix and both the spoken dialogue and the closed captions say "Ruby."