I'm gonna go ahead and start this off. I do actually think that Olivia was right. Peter should have been able to see that Altivia was not his Olivia. But I still vehemently beleive that these characters will end up together in the long run. Something will happen, and Peter will prove himself to Olivia.
I was talking to my brother about this and he brought up a really good point. Maybe the reason why Peter didn't see that she wasn't his Olivia was because he was blinded by his love. He really wanted to be with Olivia. It was so much so that he didn't see what should have been blatantly obvious.

I think you are right ! 100%
And Olivia said : "You belong with me"
So, there will be a future for them ! It has to be, because if not, I'll go to talk to them about that !

Here's the entire conversation at the end of the episode:

Peter: Olivia. You OK? What is it?
Olivia: You know what Barret said? He said that he looked into her eyes and he knew that it wasn't her.
Peter: Olivia.
Olivia: I understand the facts. I know that she had reams of information about me, and about my life and about the people that were close to me. And I understand that if she slipped up that she would have a completely reasonable explaination for it. And I guess to expect you to be able to see past that is perhaps asking a little bit too much. But when I was over there, I thought about you. And you were just a figment of my imagination. But I held on to you. And it wasn't reasonable and it wasn't logical but I did it, so, why didn't you? She wasn't me. How could you not see that? Now she's everywhere. She's in my house, my job, my bed. And I don't wanna wear my clothes anymore, and I don't wanna live in my apartment and I don't wanna be with you. She's taken everything.
(Olivia walks away)
Peter: I'm sorry.

When I read, watch or think about this scene I can not help crying

i think olivia is right, Peter knew that something was wrong but i think he was really happy with everithing that had happened and taht might affect his view.
But Olivia must understand him and how both still want to be togeter i hope that happens.