This episode begins immediately following the events of The Tangible Affection Proof, in which Raj goes out for coffee with a girl he met at the comic book store on Valentine's Day. As the events unfold, it is revealed that within minutes of arriving at the coffee shop, he'd bored her so much that she snuck out while claiming she needed to go to the bathroom.
This episode also features a new installment of Sheldon Cooper's Fun with Flags (introduced in the season 5 episode "The Beta Test Initiation", Sheldon's video podcast that provides the world with information about flags. Penny helps him with his presentation skills. When Amy explains that he should thank her, he does so, and gets an invitation to her upcoming play ... which he rudely declines. Amy then explains that he's socially obligated to attend the play.
Eventually, Raj and the girl once again connect and she reveals that she abandoned the date not because he was boring, but because she also suffers from intense social anxiety. She insists that he doesn't want to date her, but he overcomes this objection by explaining that he himself is a neurotic mess ... which, in this case, seems to actually work as a pick up line. (This approach never worked for me, but I guess that's the magic of television.)
This Episode's Science
Vexillology - This is the study of flags, which Sheldon is trying to spread through his "Fun with Flags" video podcast.
Sheldon: Amy pointed out to me that since you did something nice for me, I am obligated to do something nice for you, so, yes, I'll go to your dopey play.
Penny: Hey, I don't want you to go anymore.
Sheldon: Why not?
Penny: You should go because you want to go, not because you have to.
Sheldon: Oh, dear lord. More rules. Where does it stop? Can I want to go because I have to want to go?
Penny: Okay, do whatever you want.
Sheldon: But, no, wait. Do whatever I want? Or whatever I have to want?
Penny: Oh, for God's sake, just come to the play!
Sheldon: Okay. I don't want to, but at least that makes sense.