Plot hole: At the end of this episode Red takes off his shirt revealing his burned back, which leaves us to think that he might be Elizabeth's dad. However, this particular mark should have been noticed and written down in Red's prisoner file when he was taken into custody the first time (Episode 1). In that case Elizabeth would already know that Red is burned and could have asked some questions about it.
Character mistake: When Olivia and Dr Galina are in the bathroom, Galina mentions an umbilical chord, from a baby whose mother died (Nadia), that contained Olivia's mitochondrial DNA. Mitochondrial DNA comes from the mother, so Nadia's Mitochondrial DNA came from Letha who got hers from Marie, absolutely nothing to do with Olivia.StephNyikos