The discovery of a frozen-solid body at a construction site leads to the investigation of her death, which takes the team into unsolved cases from years past, entangling Beckett and Castle's case with a missing-persons case that was closed but never really solved.
Castle: Maybe we should be looking for ruby slippers.
Beckett: Yeah, while you're at it, why don't you should look for some flying monkeys, maybe they left her here.
Castle: People don't disappear off the face of the earth.
Ryan: Sure they do. Quantum physics, alien abductions, Schrödinger'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.
(after Alexis helps him figure out a problem with the case)
Castle: It's family moments like these I will never forget.
Alexis: With a good therapist, hopefully I will!
Castle: Alright, so you and I are married.
Beckett: We are not married.
Castle: Relax, it's just pretend.
Beckett: I don't want to pretend.
Castle: Scared you'll like it?
Beckett: That's the difference between a novel and the real world, Castle. A cop doesn't get to decide how the story ends.
Beckett: I guess your Nikki Heat has a back story now, Castle.
Castle: I don't know. I did kinda liked the hooker by day, cop by night thing. But, I guess a heavy emotional angle could work too.
Beckett: Well, don't bewilder your audience with substance on my account, Castle.
In most episodes, there is a scene that shows Beckett's personal life as she receives the call about a murder. This is one of the few episodes that begins with a scene from Beckett's personal life as she receives the call.
Watch for: Beckett taking the coffee Castle had made for himself while she's reading Melanie Cavanagh's case file. Technically this could be viewed as the first time Castle has brought Beckett coffee, despite him doing so unintentionally.
Beckett's fury with the attitude of the people that she interviews that the murder took place so long ago that she should just let it rest stems in part from her obsession with solving her own mother's murder.
This is the first time Castle and Alexis are seen playing laser tag. A game first started when Alexis was five years old.
This is the first time that Becket visits Castle at his home.
Watch for: the look on her face when she sees his spacious, luxurious apartment.
Beckett says of the experience that she feels "like Alfred in the Batcave for the first time." Later episodes will reveal she is an avid fan of comic books.
When Beckett asked Castle how he knew Alexis missed him, Castle responds, "Spidey-sense." Spidey-sense (more commonly called "spider-sense") is a precognitive power possessed by the Marvel Comics superhero Spider-Man.
Beckett tells the story of her mother's murder to Castle for the first time.
Castle promises never to reveal that it was Esposito who gave him Beckett's mother's case file. He never does.
↑A melting woman, ruby slippers, and flying monkeys are all a reference to the 1939 film, The Wizard of Oz.
↑Schrödinger's cat is a paradox devised by Austrian physicist Erwin Schrödinger in 1935, meant to illustrate a theory in quantum mechanics. And "Sleestaks" are an alien race featured in the 70's TV series "Land of the Lost"; in a later episode, Ryan asserts that this is a cop nickname for a suspect.