(Castle makes a grand appearance in his Halloween costume)
Alexis: Hey! (smiling)
Castle: Hey. I was, I was just... trying on my Halloween costume/
Alexis: What exactly are you supposed to be?
Castle: Space cowboy!
Alexis: Okay, A, there are no cows in space. B, didn't you wear that like, five years ago?
Castle: So?
Alexis: So, don't you think you should move on?
Castle: I like it!

Castle: What are you doing up so late?
Alexis: Halloween homework. The Pit and The Pendulum. The original 'Saw'.
Castle: Have you decided what you're going to dress up as, this year? Perhaps, Indira Gandhi, Amelia Earhart, woop! (points at her) Hermione?

Alexis: What exactly are you supposed to be?
Castle: Space cowboy!
Alexis: Okay, A, there are no cows in space. B, didn't you wear that like, five years ago?
Castle: So?
Alexis: So, don't you think you should move on?
Castle: I like it!

Castle's costume is supposedly as a 'space cowboy' for Halloween. This is an in-joke for Fillion fans, since his costume is essentially the same outfit he wore as Captain Malcolm Reynolds in the excellent cult SF show Firefly. The Joss Whedon created Firefly lasted one half-season on Fox but, like most Whedon creations has developed a fanatical cult following. The show was on in Fall of 2002, so actually he wore it seven years ago. He reprises the role as Reynolds in the excellent 2005 film, Serenity. Alexis' line about "moving on" is a subtle barb at fans who don't want to give up on the show, though it stands virtually no chance of ever coming back.

Beckett: Are you kidding me, is that a stake in his heart?
Castle: Looks like Buffy is visiting The Big Apple.

A stake through the heart is a classic means to kill vampires.

Buffy is a reference to Buffy the Vampire Slayer. Like Firefly, a popular series created by Joss Whedon, in which Nathan Fillion played a villain in its final season. Buffy was, as the name described, a vampire slayer, a person with inherent natural capabilities to combat vampires.

The Big Apple is a colloquial name for New York City.

Beckett: Who would go to the trouble of killing someone that way?
Castle: Lycans. they've been at war with the vampires since Lucian was murdered in the 15th cent...

Lycans is the generic name for werewolves used in the 2003 film Underworld, which has spawned two sequels so far. The series is about an age-old battle between werewolves and vampires. Lucian is the leader of the werewolves in the movies.

Alexis: Halloween homework. The Pit and The Pendulum. The original 'Saw'.
Castle: Have you decided what you're going to dress up as, this year? Perhaps, Indira Gandhi, Amelia Earhart, woop! (points at her) Hermione?

The Pit and The Pendulum is a classic 1842 short story of Gothic horror by Edgar Allan Poe, involving a man tortured by The Inquisition, via a pendulum with a very sharp blade swinging lower and lower towards him, bound immobile, and a pit which he is forced towards by moving walls. Both ideas have become well-known memes through this story.

Saw is a popular but fairly grisly horror film series.

Indira Gandhi was an influential political figure in India during the 60s through the 80s, when she served as India's only female Prime Minister. She is no relation to Mohandas K. Gandhi. Her father was Jawaharlal Nehru, an important peer of Mohandas and India's first Prime Minister.

Amelia Earhart was one of the first female aviators, the first woman to fly solo across the Atlantic, and holder of many records. She disappeared in 1937 during the Pacific leg of an attempt to fly around the world. The disappearance was the "Kennedy Assassination" of the 1930s, in that it generated many tales of "what really happened".

Hermione is almost certainly a reference to Hermione Granger, a compatriot of Harry Potter in the book series.

Landlady: Yeah, but mostly comic books.
Castle: Reminds me of an early Frank Miller
Beckett: Which Frank, Epic comic or Dark Horse years?

Frank Miller is an acclaimed creator, author, and artist for many comic books (notable creations include the reboot of Daredevil and Elektra for Marvel, The Dark Knight for DC, along with Sin City and 300 for Dark Horse). He has since gone into film direction, having assisted in the direction of the movie Sin City, based on his comic book, and a poorly received adaptation of Will Eisner's The Spirit. Both the 80s revival of Batman by Tim Burton and the more recent reboot in 2005 of the films reflect a great deal of Miller's influence on The Batman's mythos via The Dark Knight and Batman: Year One comic book miniseries

Epic Comics was a creator-owned imprint line of Marvel comic books running from the late 1980s through the mid-1990s

Dark Horse is one of the most successful comic book entities outside of Marvel and DC, with ownership of a number of wildly successful media spinoffs from already popular titles, including Aliens-v-Predator, Sin City, The Mask, Hellboy, and 300.