Howard is selected to be part of a crew to go to the International Space Station. Sheldon and Amy officially become a couple. Leonard is tired of fighting his feelings for Penny and they get back together.
Sheldon: I want to build a road, but I need wood. Either of you fellas have wood? (Raj and Howard giggle) I don't understand the laughter. The object of Settlers of Catan is to build roads and settlements. To do so requires wood. Now, I have sheep, I need wood. Who has wood for my sheep? [..] Come on, I just want wood. Why are you making it so hard?
(later) And now that I have some wood, I will begin the erection of my settlement.
Raj: (aside, to Howard) Okay, he's got to be doing this on purpose.
It's a very common joke for Settlers in real life as well.
Beware the Nice Ones: Played with. Bernadette is understandably pissed when she finds out Raj has been writing love poems about her, yet she is still nice about it.
Raj: Do you think I have a shot with Penny?
Bernadette: OF COURSE YOU DO. YOU'RE A CUTIE-PIE! ANY GIRL WOULD BE LUCKY TO HAVE YOU! (slams door)
Daydream Surprise: The entirety of "The Recombination Hypothesis" was a daydream by Leonard trying to figure out his feelings for Penny and their future. The relationship fails, but he still decides to ask her out again in real life.
Entitled Bastard: In The Wiggly Finger Catalyst Penny breaks up Raj's relationship with Emily, even though Raj was fully aware that Emily was a Gold Digger and perfectly okay with it. After Penny splits them up by telling Raj's parents, she tells him that she wants a big tip, since he's rich, at the end of the episode.
Heel Realization: Bernadette surprised herself when she realized she was wrong to try to keep Howard from taking his chance at realizing his dream.
Penny when she realized she was a bully in school and tried to apologize to the people she bullied.
Lampshaded in short order as Sheldon suggest they go to their pizza restaurant: Corleone's.
Howard: Sure, no mobsters there.
Long List: The list of things that were stolen from Sheldon and Leonard's apartment, most of which were video games.
Mildly Military: Sheldon gives himself the Paintball rank of Captain, citing Kirk, Crunch and Kangaroo as examples. He sews Army Captain's bars to his uniform, but the three he references are Navy/Coast Guard Captains, the equivalent of Army Colonels.
Mutual Disadvantage: To decide who gets Prof. Rothman's office, Sheldon and Barry play a one-on-one game of basketball, under the notion that they are equally bad at sports, putting them on an even field. It works too well, in fact, as neither manages to score once after 45 minutes.
My Friends... and Zoidberg: Sheldon refers to the rest of the group as his "three friends and one treasured acquaintance", who turns out to be Howard.
O.O.C. Is Serious Business: Howard kicking Bernadette out of the house, without wanting sex with her is a sign that he is really not happy about Bernadette going behind his back and telling his mother that he was picked by NASA to go into space.
Paintball Episode: After Sheldon's Death Seeker action in being a horrible leader, he ended up inspiring the guys to take back the game and the won the inter-department paintball game for the first time.
Relationship Upgrade: It was a real shock when Sheldon asked Amy to make their relationship official.
Rewatch Bonus: Give "The Recombination Hypothesis" a 2nd look, and you'll spot some subtle clues throughout that most of the episode is a daydream Leonard is having. The most telling clue being that Sheldon is seen flirting with Amy at one point.
Unwanted Gift Plot: Amy gives Penny a tacky painting of the two of them, insisting that it be displayed prominently in her living room. It is supposed to be hung on the fourth wall, which is why it hasn't been seen since.