Character mistake: The officers count the inmates and say there's 10 missing. There are indeed 10 inmates hiding in the pool. However, Pennsatucky and Chang had escaped the prison. The officers counted Linda as an inmate, who had been hiding in Litchfield the whole season, and wasn't on the list. That would make it 11 people missing, not 10.
Continuity mistake: In the scene where William Fichtner is shown first leaving his trailer and picking up litter in the amusement park, his gloved hand switches from his right hand to his left then back to his right again before he starts talking to the couple. (00:05:40)
Continuity mistake: Right at the beginning of the episode a Cadillac Escalade gets stolen. The car is the newest model. The chase begins and the car is a new model right up to a scene when they crash into some other cars. That part was filmed with older model Cadillac. The damage is quite severe, but the chase continues again with the new model that has only one bit of damage - a mirror that has come apart.
Continuity mistake: Near the start, the camera pans out to see the dome now covered in a layer of black. Outside of the dome you can see nice green fields, a small forest area, little houses and everything looks rosy. However a few episodes back the military launched a MOAB (mother of all bombs) and and the surrounding area was wiped out completely. (00:05:50)
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.
Other mistake: When Lucas and Zoe are at the restaurant, Zoe steals the staff list from the kitchens. It is an established fact that a waitress named Stephanie works in the restaurant, however when the camera closes on the list, her name is not listed among the other staff members. (00:32:40)