Continuity mistake: Right at the very end, Olivia comes to meet Peter at his place for drinks. While Peter goes to grab his coat, her hair moves behind her right shoulder in a consecutive shot.
Continuity mistake: When Walter tells Peter that the Cocabeans he bought can't be eaten, he takes the roasting pan off the bunsen burner. In the next shot, the pan is still on the burner. (00:06:55)
Continuity mistake: After Fauxlivia shoots Joe and is dragging him to the bathroom to dispose of the body, she hears a knock on the door. During this shot, she is dragging him with his jacket over his head, which she is gripping. However in the immediate next shot, she is still dragging him by his jacket, only the jacket is much lower.
Continuity mistake: When Walter is using the hammer on the block of ice, the pattern that results is different when viewed from each side.
6:02 AM EST - S3-E20
Continuity mistake: This is after Olivia has bumped into Walter in the hallway. She gets back into bed and tells Peter that his father is walking around the house naked. Peter laughs and says it's normal for a Tuesday. The sun is on Peter's left cheek in shots from behind Olivia. In the reverse shots from behind him, the sun is missing. (00:07:30)
And Those We Left Behind - S4-E6
Continuity mistake: While beginning to take the radiation readings of the Jeep during his time jumps, Peter has a wedding ring on his finger. After cutting away and back again, the wedding ring is no longer on his finger. (00:15:15)
Brave New World: Part 1 - S4-E21
Continuity mistake: This is when Peter and Olivia are discussing different Boston's suburbs as their potential new home. The sun is on the right side of Olivia's face in one shot. In other shots, it isn't.
Brave New World: Part 2 - S4-E22
Continuity mistake: The left side of Peter's face is alternately bathed in sunlight or not throughout the scene when he and Walter talk in front of Olivia's hospital room.
Answer: In the time line of Season 4, William Bell is trying to destroy both universes to create a new one, and he needs Olivia to power the collapse. So he helped her escape. But the real question is, if not in search of Peter, why Olivia has to travel to the alternate universe to be captured and replaced?
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