They did not write the Shae bit well, but Peter Dinklage’s acting saved them.
Wrong thread. I think you want the one for the episode of 11 May, here.
Count me amongst those thinking he didn’t recognize her after watching this scene. And amongst those thinking that he would have done something with this piece of information. I’m pretty sure that if the show makers wanted us to think he recognized her, they would have made it clear (littlefinger making a side comment, for instance).
He starts talking about her and her sister as soon as she leaves the room.
The argument for him knowing would be that in talking about the Stark girls lets the audience know that he knows.
The argument for him not knowing would be that if he did know, he would never bring up the Stark girls in front of Tywin - knowing that Tywin doesn’t know.
Who’s on first? I don’t know. THIRD BASE!
Maybe he doesn’t know if Tywin knows. Hence, he immediately brings up the subject of the girls, and very carefully watches Tywin’s reaction.
This is why I think what this show really needs is a character who turns to the audience and tells us what he’s really thinking, like on House of Cards.
Blech.
I instead think that Littlefinger noticed Arya’s behavior of listening a little too closely to what was being said, and of being more than just a servant. I think the gears in his head were thinking “Tywin has a little spy and he doesn’t know it, how amusing!”
That’s a pretty good theory, I’d say.
That doesn’t quite cover why he’s trying so hard to get a good look at her face. His expression is more suspicious and calculating than amused in my opinion.
Yeah, but to be fair Littlefinger always looks like he’s already come up with six ways to steal your gold teeth while you’re talking and is currently plotting a seventh. I wouldn’t read anything into it.
Yeah, that looked like Littlefinger’s default face to me. He always looks like that.
Well, sure. 
But still, the way he peers into her face as if trying to figure out if she’s who he thinks she is makes me think he recognizes her. He sat next to her and Sansa at the tournament, and probably encountered her at other times in King’s Landing, I don’t think a shorter hairstyle would be enough to make him not recognize her, clever little sneakypants that he is.
With the heated arguments from both sides, Littlefinger knowing/not knowing is probably kept ambiguous so as to give the writers more options down the road.
shakes fist
Martiiiin!
Just noticed that Burn Gorman, who was mutineer leader Karl Tanner on GOT, is now playing a British Army officer on the Revolutionary War spy drama Turn on AMC:
http://winteriscoming.net/wp-content/uploads/2014/04/cogman1.jpg
And Pedro Pascal, who plays Oberyn Martell, is also on “The Mentalist” playing FBI Agent Marcus Pike. It’s a little disconcerting. 
I couldn’t watch the Karl Tanner scenes without thinking of Torchwood anyway. 