Other mistake: When Peter is watching Richard Steig in the interrogation room and gets up to go in there himself, he tells Walter to stay there. On the live video screens behind him, you can see Peter enter the room before he actually does. (01:03:50)
Visible crew/equipment: When Olivia spots John taking off in his SUV, the reflection of a crew member's head is visible when she opens the driver's side door. (01:13:35)
Continuity mistake: The front license plate on John's SUV falls off during the chase with Olivia. It reappears seconds later. (01:15:30)
Factual error: When the 747-aircraft of the fake German airline is being shown, you can see the German flag on the plane. But you also see an "N-xxxxx" registration which stands for USA. If it were a real German plane, it would have a "D-xxxx" registration.
Continuity mistake: On the park bench, while talking to Peter, Olivia's hair moves back and forth over her right shoulder. (00:32:40)
Factual error: An aerial view of the "Miami Tower" (in Miami, Florida, of course) is labeled as "Boston Federal Building".
Continuity mistake: At the beginning of the episode, when Christopher is putting Loraine in the car, her stomach changes from bulging outward to flat and normal in one shot.
Continuity mistake: When Olivia says "Freshman", Peter and Walter are seen screw driving wires into Roy's head. In the next shot, the wires are gone and they are drilling in his head. Later on, they use the screwdrivers again. (00:36:30)
Continuity mistake: The bullet hole in Davidson's chest is not at all where he was shot.
The Arrival - S1-E4
Visible crew/equipment: When John Mosley, the stocking-capped man exits his car, you can briefly see the camera's reflection in the glass window behind him. (00:13:30)
Power Hungry - S1-E5
Visible crew/equipment: When they're transporting Joseph Meegar out of the building and into the ambulance, you can see the reflection of the boom mike on the open car door, (the car Charlie is putting Mr. Fischer into). (00:41:00)
Continuity mistake: This episode takes place over one day. It's Olivia's birthday at the start of the episode, and at night, she gets the card from her stepfather, implying that it's still the same day. Right before Broyles yells at Olivia in the Harvard halls, there is an establishing shot of Harvard where it is nighttime outside, but inside the building, there's sunlight coming through the windows.
Other mistake: In this episode, we discover that Olivia shot her stepfather when she was nine years old. So how could she have possibly become an FBI agent after an incident like this?
Plot hole: When Charlie looks up the file on David Esterbrook, he says that the file shows that Esterbrook is directly responsible for INtREPUS' "controversial" R&D, including pre-natal gene therapy, human/animal hybridization, and viral warfare. Yet later, Olivia says she can find no dirt on Esterbrook who is, in her words, "cleaner than snow". If INtREPUS kept records of their illegal endeavours, then how come Olivia can't find them when the time calls for it?
In Which We Meet Mr. Jones - S1-E7
Visible crew/equipment: During the shot where Walter is talking about Jimmy Hoffa while installing a light bulb, you can see the set and crew reflected on the metal part, including the audio coordinator with a boom mike.
In Which We Meet Mr. Jones - S1-E7
Deliberate mistake: Dunham comments that she works for Homeland Security. While the FBI is under the jurisdiction of the Justice Department, she works as part of a special Homeland Security task force; so saying she works for DHS is an accurate statement.
The Equation - S1-E8
Revealing mistake: The shots of Peter and Walter entering St. Claire's are recycled shots from the pilot. You can tell because their clothes change.
Continuity mistake: During one of the first shots of Olivia in the tank, you can see the reflections of lab lights on the water even though the tank is closed.
Continuity mistake: Olivia is pretending to be Raoul's friend at the bar where his brother works. When talking to the guy, her hair moves back and forth in front of her right shoulder throughout the whole scene.
Visible crew/equipment: When Oliva punches Mitchell Loeb and he collapses against the car, you can briefly see the reflection of some crew members, one wearing a yellow jacket. (00:44:00)
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?