Altlivia walks differently, too. When she approaches the group at the opera house, it's really clear. Her speech patterns, yeah, they're different, but she also is missing a kind of reserve that Olivia always displays. It's entirely likely they won't have Peter make the connection; it will likely be Olivia's niece and maybe no-one will believe her. It may last two episodes, but probably one -- I'm expecting a two-hour season premiere as well.
The only real issues I had with it were technical, but in a series about cartoon physics, it's hard to worry about logic a whole lot:
Bell says they were monitoring all communication, best not to use a cell, because the monitoring is probably how they knew about the meeting in the park. But while the more totalitarian America in the alternate universe may be monitoring cells, what would that have to do with Nina's weird, one-way email communication? And if they knew Bell was involved with a meeting at the park, why not arrest him at the hospital. Actually, I guess the notification about the park need not implicitly involve Bell, just that an email from the other side specified a meeting in the park.
Olivia's awareness of this parallel world, being in synch with it, sometimes being able to phase into it, have come only accidentally or with guidance from Walter. She was supposedly able to open the door only with the help of the other Cortexapham babies, but instead the plan became "open a crack and set up a doorstop." How does Altlivia open the crack? How does she even know what she's supposed to do on that opera house stage?