The Holographic Excitation - S6-E5
Trivia: In this episode, Sheldon and Amy are trying to decide on couples' themed Halloween costumes. Sheldon is standing in front of the dry erase board. There are 2 columns written on the board. One named "Couples I Like" and the other "Couples You Like." Under the "Couples You Like" column, one of the couples is Blossom and Joey. Blossom is the name of the television character played by Mayim Bialik in the 90s and Joey was one of her brothers.
The Fish Guts Displacement - S6-E10
Trivia: In the beginning, after talking about the Spider-Man theme, Sheldon says it's right up there after Inspector Gadget and Teenage Mutant Ninja Turtles (to which the gang chimes in "heroes in a half shell, turtle power"). Chuck Lorre, the show's creator, wrote the original TMNT theme song that they are referring to.
The Work Song Nanocluster - S2-E18
Trivia: After Sheldon mentions a molecular sieve, they go over to 4a, their apartment. 4a is a kind of molecular sieve.
The Holographic Excitation - S6-E5
Trivia: On the couples costume idea board, "Dharma and Greg" is listed. Chuck Lorre, creator of The Big Bang Theory, also created Dharma and Greg.
Trivia: During Season 3, the producers learned of a show called "The Theorists" in the country of Belarus that was a copy of this show. A lawsuit for copyright infringement would have been pointless since the production company for "The Theorists" was owned by the Belarus government. A lawsuit, however, was not needed because when the actors and actresses found out the show was a rip-off this one, they promptly quit and "The Theorists" was cancelled.
The Bath Item Gift Hypothesis - S2-E11
Trivia: Kaley Cuoco's favorite moment of Penny's is when Sheldon hugs her after receiving the napkin signed by Leonard Nimoy.
The Recollection Dissipation - S10-E20
Trivia: When Amy sings "Soft Kitty" in German she more or less translates it literally. The German dubbed version of the show uses completely different lyrics for its rendition instead of just translating the original version.
Trivia: Six years apart, Johnny Galecki and Kunal Nayyar share the same birthday.
The Bat Jar Conjecture - S1-E13
Trivia: When Leonard, Howard and Raj are contemplating who to have as the fourth member of their Physics Bowl team, Raj says, "You know who's apparently very smart is the girl who played TV's 'Blossom'. She got a Ph.d in Neuroscience or something." The girl he's referring to is actress Mayim Bialik, who plays Amy Farrah Fowler in later episodes of The Big Bang Theory. Interestingly, she is the only recurring cast member on the show that actually does have a Ph.d in real life.
The Work Song Nanocluster - S2-E18
Trivia: Penny is the only character whose original surname was never officially revealed (she took Leonard's surname when she married him). That said, a close zoom in on a package she receives in season 2, episode 18, "The Work Song Nanocluster" appears to show her surname as "Teller". The creators have said that was simply a default placeholder prop and was never meant to be legible on screen, so it's not canonically her surname.
The Excelsior Acquisition - S3-E16
Trivia: Raj's question about why so many of Stan Lee's characters' first and last names begin with the same initial (Peter Parker, Reed Richards, Bruce Banner, etc.) has been answered by Lee in interviews before: He has a bad memory for names, so if he can remember one of their names, he knows the other starts with the same letter.
Trivia: Sheldon and Leonard were named after producer/creator Sheldon Leonard, who created and produced such TV hits as the Dick Van Dyke Show and the Andy Griffith Show, as Chuck Lorre was a huge fan of his.
The Excelsior Acquisition - S3-E16
Trivia: The judge at the courthouse is named J. Kirby. Jack Kirby was a Marvel comics artist who partnered with Stan Lee, who also appears in this episode, to create The Fantastic Four, The Incredible Hulk, and many other Marvel comics.
Trivia: One of Penny's classmates, Cole, is portrayed by Ryan Cartwright. Ryan Cartwright is a main character on Alphas. At the time of the episode, Alphas hasn't been cancelled. Episode 21, The Closure Alternative, deals with Sheldon getting over learning Alphas had been cancelled.
The Cooper Extraction - S7-E11
Trivia: Penny gets her break appearing in NCIS. Kunal Nayyar who plays Raj, had his first acting job on NCIS season 4 episode 12 Suspicion. Coincidentally this is the episode prior to Penny's episode.
The Mommy Observation - S7-E18
Trivia: The car parked left from Stuart in the future sequence is a BMW i3, which is an actual production car introduced in 2014.
Answer: Because Raj's selective mutism seems to be caused by women that Raj sees (on some sort of conscious or subconscious level) as a potential sexual partner. An attribute that wouldn't apply to either his sister or mother.