Beckett's mother was named 'Johanna'

(looking at the dead body)
Beckett: She's melting.
Castle: Maybe we should be looking for her ruby slippers.
Beckett: Yeah, while you're at it why don't you look for some flying monkeys maybe they left her here.

Castle: It's kind of odd, taking the trouble to freeze a body, then dumping it? We've got two personality types working here. A killer who freezes a body is a keeper. He wants a souvenir. But a guy who dumps a body...?
Beckett: Doesn't want to be reminded of the crime.

(slapping a pile of folders down in front of Castle)
Beckett: Welcome to the department's official facial recognition database.
Castle: By hand? That's like life before TIVO.
Esposito: Maybe you could download an ap on that phone of yours...
Castle: Ahahahahahaa...there are a lot of missing people.
Beckett: One way or another we eventually find them. Some end up dead, some turn up in a double wide... with a stripper named Trixie outside Atlantic City.
Esposito: (holding a folder) And some, just don't turn up.
Castle: (reading from the folder) Dana Sullivan.
Esposito: Mmm-huh. Her and her boyfriend leave a club. He's a couple steps behind her 'cause he's got a call on his cell phone. She turns a corner just a few seconds before he does and when he comes around, she's gone. Street's totally empty, no traffic, no nothing. In a matter of three feet, she literally just "disappeared".
Castle: People don't "disappear" off the face of the earth.
Ryan: Sure they do. Quantum physics, alien abductions, Schrodinger's cat. One minute, you're getting a hot dog in the park, the next you're fighting off Sleestaks on the far side of a dimensional rift.

Ryan: Samuel Cavanaugh, shot outside a grocery store about a year ago.
Esposito: Small caliber, double tap to the chest. All valuables missing.
Ryan: Poor schlub's wife disappears, four years later he gets shot in a mugging.
Esposito: Yeah. What are the odds?
Castle: Long. Unless they're connected.
Esposito: What, four years between murders? One's a popsicle, one just got popped. How could they possibly be connected?
Castle: Maybe he and his wife got into something they couldn't get out of. Maybe something to do with a drug habit?
Ryan: So some skel waits four years to finish the job?
Castle: Maybe he finally figured out what happened to his wife, and was about to go to the police with it.
Ryan: I don't believe it.
Castle: Give me two hundred and fifty pages I bet I could make you.
Beckett: We're solving a murder, Castle, not writing a book.
Castle: I will call it, 'A Chill Runs Through Her Veins."
Esposito: Oooh. I like it!
Castle: Ah!? Ah!? Bam! said the lady, another best seller for me...

Castle: I'm just trying to figure out why someone would put a dead body in a freezer.
Alexis: Is this a 'Nikki Heat' or a 'Detective Beckett' question.
Castle: Beckett.
Alexis: Oh, that's right, the Nikki Heat thing was about incinerating a body in a self-cleaning oven.
Castle: Mmmhhmmm. I mean, you put things in a freezer to keep 'em for later, but once they're there, you rarely ever go back.
Alexis: If I was putting a body in a freezer it would be because I was trying to hide it.
Castle: Until you stop paying for the storage space.
Alexis: Did I stop, or did something stop me?

Beckett: That's the difference between a novel and the real world, Castle. A cop doesn't get to decide how the story ends.

Castle: Alexis missed me.
Beckett: How did you know?
Castle: Spidey sense.

Beckett: By the way... it was my mother. Not my father.... We were supposed to go to dinner together, my mom, my dad, and I, and she was going to meet us at the restaurant, but she never showed. Two hours later we went home.... and there was a detective waiting for us, Detective... Raglin. They found her body. She'd been stabbed.
Castle: A robbery?
Beckett: Nope. She still had her money and purse and jewelry. And it wasn't a sexual assault, either. They attributed it to 'gang violence'. A random wayward event. So just like in Melanie's case, they couldn't think outside the box. So they just tried to package it up, nicely.... And the killer was never caught.
Castle: Why do you wear the watch?
Beckett: My dad took her death hard.... he's sober now. Five years. So... (pointing to the watch) this is for the life that I saved. (pulling out a ring on a necklace) And...this is for the life that I lost. I guess your Nikki Heat has a backstory, now, Castle.
Castle: I don't know, I did like the hooker by day, cop by night, thing. (she smiles) But I guess the "heavy emotional angle" could work, too...
Beckett: Well. Don't bewilder your audiences with substance on my account, Castle.
Castle: Until tomorrow, detective.
Beckett: You can't just say 'Night'?
Castle: I'm a writer. 'Night' is boring. 'Until tomorrow' is more... hopeful.
Beckett: Yeah, well. I'm a cop. 'Night'.

Beckett: She's melting.
Castle: Maybe we should be looking for her ruby slippers.
Beckett: Yeah, while you're at it why don't you look for some flying monkeys maybe they left her here.

"She's Melting", Ruby Slippers, Flying Monkeys, all references to the Wizard of Oz, its heroine, Dorothy, and the story's villain, the Wicked Witch of the West.

Beckett: One way or another we eventually find them. Some end up dead, some turn up in a double wide... with a stripper named Trixie outside Atlantic City.

A double wide is a type of mobile home/trailer/"manufactured housing". It has connotations of low-rent, low-brow, and lower class.

Ryan: Sure they do. Quantum physics, alien abductions, Schrodinger's Cat. One minute, you're getting a hot dog in the park, the next you're fighting off Sleestaks on the far side of a dimensional rift.

Quantum physics is nominally possible as an explanation for a disappearance. It's theoretically possible for all your atoms to suddenly disperse and fly off in different directions. Not likely, though.

Alien Abductions is also nominally possible as an explanation for a disappearance. Who knows what technology aliens might have access to, including something akin to Star Trek's teleporters...? Again, not likely, though.

Schrodinger's Cat is a bit more "iffy" reference, presumably also tied to quantum physics and the role of the observer in any scenario. One could presume under quantum physics that a person's entire body could just randomly "decide" to be somewhere else, possibly anywhere in the universe. Really not likely, however.

Sleestaks are the bad guy aliens in the 70s cheesy sci-fi show Land of the Lost, which posits a sort of "dimensional rift" through which one entered the Land of the Lost from our world.

Beckett: How did you know?
Castle: Spidey sense.

Spidey Sense is the term for a preternatural capability to sense things attributed to the comic book character Spiderman. In general, it usually provides a warning premonition of danger.