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.
Night of Desirable Objects - S2-E2
Revealing mistake: When the typewriter is being used at the end, the keys being pressed don't correspond to the words appearing on the paper. Obvious from the start - the first letter pressed is on the middle row of the keyboard, but the first word typed is "unacceptable".
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?
AmiSecured