Dream references one of the famous lines from T.S. Eliot's poem The Waste Land, "I will show you fear in a handful of dust."
Read The Waste Land with annotations at Bartleby.com.
The two brothers are DC Comics' Cain and Abel, based on the Biblical characters of the same names. From the 1950s through the 1980s, they were the respective hosts of DC's horror anthologies House of Mystery and House of Secrets.
The Sandman reinvents them as more mature, developed characters who have been transported to The Dreaming as storytellers, where Cain seems compelled to continually murder his brother in a reenactment of the Biblical story. Cain's pet gargoyle, Gregory, is transformed into a much larger beast.
Read the original story in Genesis chapter four at Bible.com.
The gates of horn and ivory are a literary image used to show whether dreams are of factual or false events. Because of the similarity between the words "horn" to "fulfill" and "ivory" to "deceive" in ancient Greek, true dreams were said to come through the gates of horn and false dreams to come through the gates of ivory.
The expression dates from Homer's time, its first use being in book 19 of The Odyssey.
The Arkham Asylum for the Criminally Insane is a prison/sanatorium located on the outskirts of Gotham City in the DC universe. It houses a large number of Batman's nemeses, as well as other criminals who have been declared insane.
A major sequence in the recent movie Batman Begins takes place in Arkham.
John Dee, or Doctor Destiny, made his first appearance in 1961 as one of Green Lantern's enemies, and went on to battle the Justice League of America multiple times. He is named after a noted occultist and consultant to Queen Elizabeth I, but does not seem to be intended to be the historical figure himself. His mother Ethel Dee, formerly Ethel Cripps, is Gaiman's creation.
Lucien was originally the host of a three-issue horror anthology comic called Tales of Ghost Castle, published in 1975.
This refers to the character Eve, who was often seen with a raven in her early appearances with her sons, Cain and Abel.
Hecate, or Hekate, was an ancient Greco-Roman goddess associated with witches, magic, and death. Over time she came to be represented with three faces, three heads, or three separate bodies, to represent various facets of her personality or function. She also made up one third of the Italic goddess Diana Nemorensis, who was made up of divine huntress, moon goddess, and goddess of the underworld.
Gaiman fuses Hecate with the three major Norns, maidens from Norse mythology who controlled fate, called Urth, Verthandi, and Skald (or Urd/Wyrd/Fate, Verdandi/Present and Skuld/Future), as well as the more commonly known Fates from Greek mythology, called Clotho, Lachesis, and Atropos. The three witches from Shakespeare's Macbeth evoke the same idea.
Gaiman uses several common depictions of the Fates in his characterization, including their being voracious eaters, having interchangeable bodies or personalities, and being represented as three stages of womanhood: the maiden, the mother, and the crone, or a variation on those three.
The Fates also refer to themselves as Morrigan, an Irish triple goddess made up of Badb, Macha, and Nemain, three war goddesses; three avenging sisters in Greek mythology named Tisiphone, Alecto, and Megaera; the three members of the 1960s vocal group The Supremes: Diana Ross, Mary Wilson, and Florence Ballard ("Candy" referring to a replacement member named Cindy Birdsong); and Mordred, Mildred, and Cynthia, the three witches who hosted DC Comics' 1970s horror anthology The Witching Hour. One of the women indicates that Mordred's name was meant to be Morgaine, both names of characters in the legend of King Arthur, but Mordred, the illegitimate prince, was confused with Morgaine, the witch.
Hammer Film Productions was a United Kingdom-based film company famous for the low-budget horror movies it produced in the 50s, 60s, and 70s.
There is also a DC Comics villain called Circe, a sorceress usually set opposite Wonder Woman. Her first appearance was in Wonder Woman #37 in the 1940s, and she is still active today. The Fates could be referring to either version of the character, since no version of them has any documented rivalry with either version of Circe.
John Constantine is an occult detective who first appeared in Swamp Thing #37 in 1985 and now stars in his own Vertigo series, Hellblazer.
The Justice League of America is one of DC Comics' central superhero teams, usually counting Superman, Batman, Wonder Woman, Green Lantern, and the Martian Manhunter as members, as well as a variable roster of other heroes. Green Lantern and Batman are the heroes pictured taking the ruby from Doctor Destiny.