Just in case I get some people who read my previous post and think "Well, the two Olivias look identical.", let me disabuse you of that right now. The two Olivias look NEARLY identical, but other than that they're two different personalities. Even though Red dyed her hair, she still is nothing like Olivia.
Now to the dumbing-down. Walter, in several episodes, could deduce Olivia's moods even when she wasn't saying anything. He spent two years with her, he should know her in and out, and as I said, Red is nothing like Olivia. He's a genius, trained to observe since he's a scientist and he can't tell he has the wrong Olivia? Give me a break, he should have noticed within a day or two. Writers have dumbed him down.
Peter, in the S2 ender, was talking to Red and telling her that he liked her hair better (though his tone of voice and facial expressions said otherwise). He also mentions that, while they do look nearly identical, one of the Olivias (can't remember which he said) had darker eyes than the other. Now, back in Blue universe and half a season is nearing and he hasn't noticed the difference in eye tone like he did upon first meeting? Dumbed-down, he should have noticed within a day or two, after all, he's also a genius, son of a scientist and a scientist himself, so he should be that observant.
It's writer contrivance to keep Red in the BlueVerse for a longer period of time. She should not have been able to fool them for that long, she was sent over there knowing nothing about Olivia except what she gleaned in that short meeting at her place where they fought before Olivia dyed her hair to pass as Red to go get Peter. Red does not have a photographic memory, Peter should have noticed her hesitation in the last episode when he asked for the list of numbers, he should have noticed when she appeared not to remember the bookseller, he should put two and two together and realize that shapeshifters keep dying around her before they can capture them and that their dorsal doohickeys are mysteriously being rendered unusable. The clues are there, the writers have Walter and Peter blind to them, even though they're the most observant of people otherwise.
Writers, Walter and Peter are FUBAR so far, I hope it gets better.