Accidental Marriage: Penny had one of those with Zach in Las Vegas. She does not realise she is legally married - she was so drunk she wrote it off as "one of those joke weddings you have in Las Vegas". Leonard is suitably mortified; Sheldon helpfully points out that while stone-cold-sober, Penny has turned down three proposals from him.
But accepted one.
Actually Pretty Funny: Amy doesn't think any of Sheldon's attempts at humor are very funny, until he drops his pants and she starts laughing.
Adam Westing: In "The Convention Conundrum", James Earl Jones befriends Sheldon and takes him on a wild night on the town, revealing himself to being a Star Wars geek and prone to playing practical jokes on Carrie Fisher, who turns out to be a little crazy herself.
Wil Wheaton bemoans the way his career has been going in "The Indecision Amalgamation". In The Tag, he has a role in Penny's movie, as the orangutan she has to wrestle with.
"The Gorilla Dissolution" shows that he got upgraded to Penny's love interest. When he gets fired for standing up for Penny, he gladly takes an audition for Sharknado 2.
Anti-Climax: Leonard and Penny's engagement was not nearly the big romantic gesture either of them were expecting or hoping for; it was at the tail end of an argument about what the other person wanted and they both eventually came to the conclusion of "Why not." Lampshaded by them, and then Leonard remembers a ring he kept in his wallet to bring it back around into something special.
The Bechdel Test: Referenced indirectly in the season premiere. Amy and Bernadette complain that they never get to talk about their academic/scientific endeavors because Penny is usually with them, and she usually just wants to talk about guys.
Bedmate Reveal: In "The Relationship Diremption", Sheldon wakes up next to a geology book.
Blatant Lies: Sheldon keeps insisting that he doesn't miss Leonard and that he's the one comforting Penny, not the other way around.
Catapult Nightmare: Sheldon when he dreams about Leonard being attacked by a kraken, although he's more disturbed about the DVDs of Back to the Future II and III being in the wrong boxes.
The Chain of Harm: At the end of "The Itchy Brain Simulation", after Penny sets Raj up with one of her friends and the date goes horribly.
Friend to Penny: What is wrong with you?! Penny to Raj: What is wrong with you?! Raj to mirror: What is wrong with you?!
Chasing A Butterfly: When Sheldon goes missing in "The Status Quo Combustion", Leonard tracks down his phone, a precaution he took ever since Sheldon wandered off chasing after a balloon at the swap meet.
Continuity Nod: A surprising number of them for a show that previously prided itself on being very self-contained in each episode. "Table Polarization" brings up the story of how Sheldon found his spot in season three's "Staircase Implementation" after Leonard brings in a couch to replace the lawn chairs Sheldon used previously, all as evidence that Sheldon is not as against change as he claims. "Indecision Amalgamation" also references the same episode in how Sheldon was excited for the Zune, not knowing how firmly it would be trounced by the iPod.
Deliberately Painful Clothing: The itchy sweater in "The Itchy Brain Simulation", which Leonard has to wear (with nothing underneath) until he can return a rented videotape, to show him how Sheldon feels about not having closure.
Does This Remind You of Anything?: In "The Relationship Diremption", Sheldon treats giving up studying string theory like breaking up a relationship, as per Penny's suggestion. The analogy even extends to him having a regretable "one-night stand" with geology, which he considers "the Kardashian of sciences".
invoked"The Hesitation Ramification" has Sheldon trying to learn about humor, but his attempts at telling jokes fall flat, especially when Penny gets depressed after her one scene on NCIS gets cut.
Sheldon: [Shortly after Penny leaves] I've been studying comedy, and they say comedy equals tragedy plus time. [looks at watch for a few seconds] Let's tickle some ribs.
It gets played with in the last scene when Sheldon conforts Leonard after Penny's failed marriage proposal probably caused them to break up. Leonard is actually surprised that Sheldon didn't try to make an inappropiate joke, but then after he pats Leonard on the back...
In "The Thanksgiving Decopulation", Amy childes Sheldon for comparing being dragged to Mrs. Wolowitz's house for Thanksgiving to being made a slave.
Fake Shemp: In-universe. When Penny gets fired from the Serial Apist movie, she objects on the grounds that she's the main character. The director points out that she just shot the last scene in which her face is shown, and that the rest of the film will feature another actress in a gorilla mask and blonde wig.
Fat Suit: One of the what-if scenarios in "The Cooper Extraction" is of Leonard getting fat from being pampered by Raj. Stuart and Raj also become fat as the sequence continues.
Formerly Fat: Played with. In "The Mommy Observation", Rajs claims that he was fat as a child and so got by telling stories and planning mystery parties in the hope that one day he could share them with friends. Leonard then says he saw pictures of him as a child and he was not fat, to which Raj confesses that he was "svelte like a gazelle".
In Another Man's Shoes: Sheldon makes Leonard wear an itchy sweater to show him how his obsession with closure is like an itch in his brain he can't scratch. He even mentions this phrase, stating that it's metaphorical, as Leonard can't literally wear Sheldon's shoes for having "feet like a toddler".
Insurance Fraud: Invoked in "The Status Quo Combustion". When the comic book shop burns down, everyone assumes that Stuart did it for the insurance money, including the insurance company, the person's mother and Howard.
Moral Myopia: The girls repeatedly go to Penny with their problems but the moment she needs a shoulder to cry on they quickly get annoyed by her complaining.
N-Word Privileges: When watching Star Wars Episode I, Penny agrees with the others that Jar-Jar Binks is stupid, only for them to get offended and Raj saying that only they are allowed to do that.
Noodle Implement: In “The Relationship Diremption” Sheldon wonders why there is a Geology book in the apartment as there's no reason there should be. Sheldon doesn't think it's a real science and Leonard has never shown any interest in it. Of course Sheldon wakes up next to the book after a night of drinking See Bedmate Reveal above.
The Obi-Wan: The recently deceased Professor Proton is not ecstatic at all about returning to act as Sheldon Cooper's literal Obi-Wan. Especially when he realises he is dressed for the part, has to have the character explained to him, and realises that note in what may be one of Sheldon's dream sequences, but this is left nicely ambiguous he is now Sheldon's spiritual advisor. he does find the light-sabre to be cool, though.
"The Reason You Suck" Speech: Penny gives Lucy a brutal one in "The Itchy Brain Simulation", mainly calling her out for bailing too easily in their relationship. She even flat out calls her a bad person.
Scar Survey: When Emily mentions that she has tattoos, Raj says he has a hole on his belly that might be a piercing. She offers to show him her tattoos if he showed it to her.
Self Insert: Stuart starts inserting himself in the other's fantasy scenarios in "The Cooper Extraction".
Shout-Out: Raj maintains that Sherlock Holmes is really Indian as he was stolen from an Indian detective character. This echoes a recurring character in British-Indian comedy show Goodness Gracious Me who insists everything is Indian.
Sherlock Holmes? Indian!
Spirit Advisor: Arthur Jeffries (Professor Proton) appears in Sheldon's dreams in "The Proton Transmogrification" after the real Arthur passes away. Sheldon imagines him as Obi Wan in The Empire Strikes Back, much to Arthur's confusion. ("Why am I in a swamp, dressed like Friar Tuck?")
Stage Names: In a notable aversion, Kaley Cuoco got married mid-season and is officially Kaley Cuoco-Sweeting, and she proudly had her name changed in the credits at the start of an episode.
Start My Own: When the gang can't get tickets to Comic Con in "The Convention Conundrum", Sheldon decides to start his own convention rather than go with the other's plan to buy scalped tickets.
Take-That Kiss: Sheldon kissing Amy in "The Locomotion Manipulation" was originally intended as this, but it became something more.
There's No "B" in Movie: Penny was in a B-movie called Serial Apist, about a Killer Gorilla. She later has to take a part in the sequel, where her character becomes a human-gorilla hybrid.
Third Rail: Eric in "The Locomotion Manipulation", a fellow Rail Enthusiast that Sheldon meets while on what is supposed to be a Valentine's Day dinner with Amy. Sheldon invites him to his table, much to Amy's chagrin.
This Is Going To Be Huge: In "The Indecision Amalgamation", Sheldon debates whether to buy an X-Box One or a PS4. Just as he thinks he's made a decision, he realizes that many of his previous decisions ended up being for the losing format - Betamax over VHS, HD-DVD over Blu-Ray, Zune over iPod.
Toilet Humor: In "The Relationship Diremption", Howard once had an embarrassing date with Raj's date Emily, in which he clogged her toilet, earning him the nickname "Clogzilla".
"The Hesitation Ramification": Depressed at having lost a big acting job, a drunken Penny proposes to Leonard. Leonard just says "Um...", which Penny does not take well. The episode ends with them seemingly broken up for good.
Followed by "The Occupation Recalibration," Penny sobers up and is okay with the proposal incident, although new problems are introduced because Penny chooses to quit her job so she can focus on her acting career. This causes different types of stress because the burden of keeping Penny afloat without a source of income falls on Leonard, who struggles to be genuinely supportive while thinking her actions were rash.
"The Locomotion Manipulation": In a rant about being romantic, Sheldon kisses Amy as an attempt to mock her, only to linger for a moment, suggesting he liked it better than he expected.
"The Gorilla Dissolution" ends with Penny and Leonard getting engaged.
Season finale "The Status Quo Combustion": Sheldon is overwhelmed by all the changes in his life and decides to travel around in trains until he can clear his head. Also, Stuart's comic book store burns down and he takes a job taking care of Mrs. Wolowitz.
What If?: "The Cooper Extraction", where the gang, inspired by It's a Wonderful Life, imagine what their lives would be like if they never met Sheldon.
"World of Cardboard" Speech: An interesting version, done between both Leonard and Penny in "The Gorilla Dissolution." Penny loses her one, mediocre acting job and starts to take stock in where her life is going. She suggests to Leonard they should get married, and Leonard gets a turn to tell her he doesn't want to be the safe, responsible decision "like a bran muffin" but wants her to be excited like you would be for "a Cinnabon or a Pop Tart." When he says she's just depressed over losing an acting job, she rebukes that by explaining that she's thinking clearly on what she really wants and that is to spend her life with Leonard.
Leonard: Well what do you want? Penny:I want YOU, you stupid Pop Tart!