(Beckett is looking at him appraisingly as he approaches her after shooing Alexis off to school)
Castle: What?
Beckett: Nothing. (he nods his head) It's just that I'm so used to you acting like a twelve-year old all the time it's kind of refreshing to see you as a father.
Castle: Makes you want me, right?
Beckett: ...Aaand there's the twelve-year old again.

Esposito: ...Apparently, he likes to hit women.
Castle: Look at this guy, if I was a woman, I'd just... hit him back. Does he look like a killer to you?
Beckett: Everybody looks like a killer to me. Job requirement.
Castle: (moves in, threatening look on his face) Do I look like a killer to you?
Beckett: Yes, you kill my patience.

Beckett: How did you kill her?
Skye: I told her to do the world a favor and drop dead. And then she did. It's funny, she usually doesn't listen to me.

(Alexis is deconstructing the meaning behind the lyrics of Hayley's last song)
Martha: Oh, oh, that reminds me of sitting down with Lisa Olson and trying to decode The Beatle's lyrics. Playing the record backwards to see if Paul was dead.
Castle: Who can forget the countless hours I spent pondering the lyrics to Van Halen's Hot For Teacher?

Title: Famous Last Words

Famous Last Words is a term tied to irony in death, the notion typically being of someone who does something foolish saying nothing will happen, and gets killed as a result of it. Someone exclaiming that a "hot" electrical wire wasn't dangerous, "You just have to know how to handle it" and immediately getting electrocuted by it. A noted example is a Civil War officer, who, hearing his men complaining about sniper fire, stood up and exclaimed "They couldn't hit the broad side of a barn at this dist---" at exact which moment a sniper literally blew his head off.

Martha: Oh, oh, that reminds me of sitting down with Lisa Olson and trying to decode The Beatle's lyrics. Playing the record backwards to see if Paul was dead...
Castle: Who can forget the countless hours I spent pondering the lyrics to Van Halen's Hot For Teacher?

The Beatles are possibly the most influential band in Rock history. During the late 60s there were rumors that Paul McCartney had been killed and replaced by "a lookalike". There were supposed claims that some of the albums, when played backwards, said things.

Van Halen is/was an exceedingly popular band, who peaked in the mid 80s. One of their most popular hits was a song about having a sexual attraction to one's teacher, making it an instant anthem for horny teenaged boys. Add to that a fairly hot MTV video with bikini clad teachers dancing on their desks, and you get a classic for the times. The lyrics weren't entirely unworthy of consideration, either -- in one subtle passage (by the delivery alone) the lead singer, David Lee Roth, exclaims, "I'm Baack!" then "I brought my pencil!" then "Gimme something to write on, man!". If you consider it as a sexual allusion, it's reasonably intelligent.

Castle: And Tarot Cards Death isn't 'Death', Death means 'Change'
Beckett: OK, so she wasn't hiding from Death, she was hiding from Change.
Castle: She hated Obama!

During the US Presidential election, one of Barack Obama's campaign slogans was "Hope And Change", and that was one of the more popularly embraced ones.