Alternative Character Interpretation: Lord Asriel. Is he a callous would-be dictator? A misguided freedom fighter? An amoral ubermensch? An anti-hero? An anti-villain? Even Pullman sometimes seems to be at odds over this character.
Anvilicious: In The Amber Spyglass, the series' commentary on the evils of mindlessly deferring to authority, God included, becomes impossible to ignore. This obviously pushed away certain readers, while others argue that Some Anvils Need to Be Dropped.
Complete Monster: Metatron was once a human named Enoch that turned into an angel by The Authority to act as his regent. Despite his fanatical demeanor, having attempted to kill his own brother Baruch for being gay, he is revealed to be extremely power-hungry, as he turns on The Authority and traps him in a crystal. Under his stewardship the already fanatical institution of the church was prompted to commit several atrocities across the multiverse, ranging from mass Mind Rape of children to the genocide of both human groups and non-human species. Metatron became increasingly convinced that Lyra was the new Eve, so he planned on inquisitions across the Multiverse. Killing Baruch for once and for all, he marched his troops against Lord Asriel's rebel forces in a flat-out apocalyptic battle.
Death of the Author: Interviews with Philip Pullman show that this is his view of how his books should be regarded ("I don't think it's the task of the author of a book to tell the reader what it means.")
Shortly after they meet, Will and Lyra question why "electricity" refers to what is called "ambarism" in Lyra's world, and why the stone called "electrum" in Lyra's world is called "amber" in Will's. Though neither child realizes the connection, the evolution of both terms alludes to the fact that the first observations of electricity (in our world, anyway!) came from pieces of amber imparting static charges to feathers and other small particles.
The daemons themselves are rooted in Greek mythology and philosophy: there is a story mentioned by Platon as well that way back when, humans weren't singular entities like today but like conjoined pairs of twins called androgynes- since most were a pair of man and woman but there were in fact man-man and woman-woman pairs as well. The gods, however, fearing the power the androgynes might have, separated them, creating the current status quo, and it is said that if you find your soulmate, it's the person who was your other half before you were torn apart.
"Holy Shit!" Quotient: In The Amber Spyglass we get a battle scene in another dimension between armies composed of angels, witches, ghosts, cosmic horrors, interdimensional aliens, jet fighters, at least one Physical God as well as God himself, badass lilliputians, steampunk airships, soldiers armed with rifles, machine guns, flamethrowers and poison gas guns, monsters, animal spirits, floating fortresses, thunder and lightning, and, of course, armored polar bears. It is undermined - intentionally - by the fact that the battle is not really focused on. Instead the story follows the two protagonists' brief appearance where they search for their daemons before killing God and hauling ass.
Unfortunate Implications: As a Reason.com review pointed out, it's kind of ironic that Phillip Pullman labels other works like Narnia as sexist and full of class snobbery, when Will, the male hero, is the one who gets to fight the most and even becomes The Chosen One in control of the mystical Subtle Knife, while Lyra's greatest feats are accomplished by "feminine" wiles like lying and manipulation. The class snobbery manifests in that Lyra is the (illegitimate) daughter of aristocrats and is vastly superior in intellect and wits than her friends in Oxford (who also happen to be the children of servants) and Will is the son of a Royal Marines officer from the beginning.