For a show that is mainly episodic and is primarily formatted so that it can be watched in any order, it surprisingly has very good continuity, almost to the point of being a full-blown story arc, as you can see by this littlelist here:
The teleportation spell "Razzamafoo" is used in two different episodes by two different magic-users.
In the Magic Man episode, Finn pulls out his autotune singing voice that he acquired by swallowing a computer right before "The Jiggler". Jake mentions that he "can never take [Finn] seriously when [he's] singing."
And he pulls it out again in "Another Way".
In "Evicted!", Finn throws the Enchiridion at a worm.
In "Crystals Have Power", Tree Trunks returns, and we finally find out just what really happened to her after she ate the Crystal Gem Apple. Also, Jake talks about being hopped up on magical power - which happened to him in the previous episode.
Because Finn lost his sword in the black hole in "The Real You", he got a new sword with a wooden hilt (which he obtained from the train in "Mystery Train").
Finn and Jake pass their gauntlet dock from "Business Time" while pursuing the Lich in "Mortal Folly". Billy's defeat of the Lich (mentioned in "Billy's Song") is also stated as the reason the Lich was imprisoned in amber: Billy pummeled him into it. The gauntlet dock also makes another appearance near the end of "Billy's Bucket List".
The "other secret room" that Finn, Jake, and Princess Bubblegum go to to discuss plans to defeat the Lich is the secret room from the beginning of "The Enchiridion!". PB was probably even holding the very same orb.
In "Henchman", Marceline returns. Also, the Duke of Nuts refers to his infant son as "my second son." This is as opposed to his first son, the Marquis of Nuts, who is seen in "The Duke".
Lady Rainicorn's parents in "Her Parents" use the same kind of translator devices that Lady herself uses in "My Two Favorite People". Theirs seem to have better settings though.
"It Came From The Nightosphere" features Marceline's song "Daddy, Why Did You Eat My Fries?", which the Ice King does a hilarious rendition of in "Holly Jolly Secrets".
In the former episode, Lumpy Space Princess calls "Drama Bomb" when things take a dramatic, emotional turn. Jake later does the same in the latter.
Also in the former episode, the Marauders from "Memories of Boom-boom Mountain" are seen again.
In the pilot, Finn says he is twelve. In "Mystery Train" he turns thirteen. Later, in "Mortal Recoil", he says "Thirteen years old? That's how old I am."
In "Memory of a Memory", Finn and Jake have to enter Marceline's memory to retrieve a spell. Soon they come to the memory of her dad eating her fries. Finn promptly says to him, "Yo, man..... don't eat those." Marceline catches him anyway.
On the counter, there's some money that's relatively untouched by the decay. One of the lyrics to The Fry Song is "I bought them, and they were mine."
"Too Young" shows that Princess Bubblegum is still 13... until the end of the episode at least.
"The Monster" is a continuation from "Heat Signature". At the start of the episode, Finn says, "I know where Lumpy Space Princess is! She's still in the woods eating beans." The episode also explains why Lumpy Space Princess has been living in the woods, thus concluding the "LSP lives in the woods" saga.
Also, "The Monster" makes a nod to "Go With Me," when LSP is living with the wolves, she runs with them and howls at the moon the same way Marceline and Finn did in "Go With me," (probably the same wolf pack too.)
Because of Ice King's Enemy Mine in the season two finale, he tries his hardest in season three and onwards to be a good friend to Finn and Jake, as shown in "Hitman" and "Still".
That wad of Princess Bubblegum's hair in "What Was Missing" is most likely the wad of hair from "To Cut a Woman's Hair".
The episode takes place in Red Rock Pass from "It Came from the Nightosphere."
In "The Creeps", Jake makes a few nods to "Mystery Train".
Jake: I GOTCHA, dude! TWO FOR TWO!
Lumpy Space Princess references "Trouble in Lumpy Space" by mentioning Brad and their break-up.
In "From Bad To Worse", Finn and Princess Bubblegum state that this is the second time a Zombie Apocalypse has happened in the Candy Kingdom, making a nod to "Slumber Party Panic".
In "Beautopia", Susan Strong returns; she, Finn, and Jake revisit the Hyoomans. Also, Jake mentions that she tried to eat Peppermint Butler.
In "Mortal Folly", Finn's blond hair is shown to have grown back after he shaved it all off for the tree sprite earlier that season. Later, in season 3 episodes "Beautopia" and "No One Can Hear You", we see that it's grown out some more and is now chin length.
In "Thank You", Finn wears the sweater that Princess Bubblegum made for him in "Mortal Folly".
In "No One Can Hear You", Finn asks if everybody's at church worshipping Glob, explaining Lumpy Space Princess's "Oh my Glob!"
"The New Frontier" explains that Glob is the final judge of a person's sins in the afterlife.
In "Wizard Battle", we see Bufo and several of his apprentices, each with a varying number of stars on their robes.
There's also the Forest Wizard from "My Two Favorite People" and "Storytelling".
"Holly Jolly Secrets" includes a mostly-naked balding man with glasses who first appeared in "City of Thieves" and returned in "Blood Under the Skin" and "Wizard Battle". The latest episode names him "Phil", as he's a Creator CameoRunning Gag based on designer Phil Rynda. A related running gag involves Phil's face popping up in other episodes, such as the seal Finn uses as a portal to the Nightosphere.
In "Marceline's Closet", Finn alludes to "What Was Missing" by questioning the idea of jamming with Marceline without the inclusion of Princess Bubblegum and Beemo.
Marceline also says she hides in Finn and Jake's house all the time, which matches her entrance in "Go With Me".
In "Incendium", the wad of Princess Bubblegum's hair from "To Cut a Woman's Hair" and "What Was Missing" returns yet again.
The season four episode "Hot to the Touch" can easily be titled "Incendium Part II" (heck, it starts where Incendium ended). Also, NEPTR returns (after a FIFTEEN MONTH game of hide-and-seek) and the goblin kingdom from "The Silent King" is seen again.
In "Dream of Love" it is revealed that Tree Trunks and the Pig from "Apple Thief" are now dating, nodding to "Apple Thief". Their relationship was foreshadowed in "Holly Jolly Secrets" (Part II).
The Nightosphere two-parter ("Return to the Nightosphere" and "Daddy's Little Monster") is obviously a sequel to "It Came from the Nightosphere". Finn remembered the Latin chant and used it to get back to the Nightosphere.
In "In Your Footsteps", the Enchiridion returns yet again. At the end of the episode, the bear gives it to the Lich, who is still inside the snail.
Jake mentions that PB is Finn's ex-girlfriend, but Finn denies this, saying they never truly went steady.
"Princess Monster Wife" briefly shows Günter's offspring which has not been seen since "The Chamber of Frozen Blades".
Princess Bubblegum created Goliad because of the events of "Mortal Folly" and "Mortal Recoil".
At one point in "Beyond This Earthly Realm" Finn calls the Ice King "Simon". In the same episode, the Ice King's Wizard Eyes from "Mortal Recoil" are key to the plot.
In "Gotcha!", LSP is still living in the woods. More of a discontinuity really, since she went back to her parents in "The Monster". The creators have explained this by saying that she's only visiting the woods and she didn't actually run away again.
LSP is seen wearing a bag from Squeeze-E-Mart, a convenience store from "Ghost Princess".
During the first few minutes of "Princess Cookie," as Finn and Jake discuss their plan with Princess Bubblegum, you can clearly see Goliad and Stormo sitting on a castle turret in the background, still locked in psychic combat.
One of the patients at the mental hospital is the Royal Tart-Toter from "The Other Tarts".
"Sons of Mars" is the episode for long-time fans. Magic Man returns, and Mars is visited. And Abe Lincoln's on it.But Wait, There's More! "It's the dog! The one we were prophesized to meet!!" Grob Gob Glob Grod says this line right after Jake dies. Guess Jake's croak dream came true after all!
And that's still not all. The concept of "dead worlds" returns; in this episode the 37th dead world is seen, while in "Ghost Princess" the eponymous character mentions transcending to the 50th dead world. Also, Death returns.
"Burning Low" is the third episode in the Flame Princess "arc". Princess Bubblegum reveals why she had Flame Princess trapped in that lamp.
The title card is also reminiscent to that of Incendium's, only this time, it's PB crying over pictures of Finn.
The Morrow returns.
At the beginning of the episode, the trio is at the site in which "Memories of Boom Boom Mountain" takes place. The marauders have left their village and you can see Finn burning the village (a marauder helmet was one of the things tossed in the fire.) Apparently, we'll find out what happened to them in a future episode.
Ever since "Dad's Dungeon" Finn has been using the demon blood sword.
NEPTR returns in "BMO Noire" trying to buddy up with BMO.
"King Worm", like "Sons of Mars", is full of continuity nods. First of all, and most obviously, the giant crowned worm from "Evicted!" returns.
The mysterious ghost lady from "The Creeps" returns, still locked in Finn's subconscious.
Fear Feaster opens up the vault to Finn's fears, showing that he still lives in Finn's belly.
Also from "Ocean of Fear", Finn is still afraid of the ocean.
Other recurring characters are the Lich, Joshua, Flame Princess and Phil.
"Mirror Finn" is reminiscent of (but not identical to) the vision Finn had of his future self in "Mortal Folly".
Lady Rainicorn's second mouth is the one she had in the pilot.
Ice King calls Finn and Jake Fionna and Cake.
Princess Bubblegum makes a nod to "Too Young".
The mushroom cloud that appears in the coffee cup as she says this is the same as when the Lich reached his well of power.
Finn is still shown to be afraid of being helpless and alone, matching his song in "What Was Missing".
Princess Bubblegum: You wouldn't understand. You're too young.
Finn is shown to still be scared of clowns, which connects to "Another Way".
Andfinally, the ending scene almost perfectly mirrors the ending scene of "Evicted!"
In "Lady & Peebles", Ricardio returns, and so does the topic of Zanoits and their poison.
Ricardio refers to Ice King as Simon as he steps over him.
Lady also uses her intangibility again.
Lady mentions that she's already been attacked by zombies twice.
PB tells Ricardio that she knows a "thing or two about creating a body out of biomass," an obvious reference to three of her science experiments: Goliad, Stormo, and Lemongrab.
"The Lich" marks the return of the titular character, after being stuck for two seasons in the snail form. Also Billy, a character from season 1 and hero before Finn's times, teams up with the main character to defeat the Lich. And that's probably not the end of it.
Obviously as part of a string of events foreshadowed by "King Worm", another call back to the episode (or foreshadow from the episode pops up. The Finn seen in the mirror in "King Worm" is actually the alternate universe Finn we see at the end of "The Lich".
In "Five More Short Graybles", Finn and Jake are trying a "spell" that involves poking things, at one point Jake pokes Lady Rainicorn's now obvious baby bulge.
"Up a Tree": Baby bulge. Again.
In "All the Little People," Jay T. Dawgzone (here spelled "Doggzone")'s book Mind Games comes back yet again.
Finn uses the tiny computer he swallowed to change his voice in "Davey". The closing gag is also a callback to "It Came From The Nightosphere".
In "Mystery Dungeon" the Ice King's fanfic "Fionna and Cake" plays a major role in the plot.
Tree Trunks says that "one of" the Lemongrabs is there, referencing "You Made Me."
And due to NEPTR and Ice King being together, we're given a nice helping of references to "What is Life?"
"All Your Fault" is a Sequel Episode to "You Made Me." Is there an arc of Lemongrab episodes going on here?
Lemongrab-original is still hungry from "Mystery Dungeon", and it's here that we learn why!
In "Little Dude," Finn has a shaved head. This is because he shaved his hair in "Davey."
The Ancient Sleeping Magi of Life-giving from "Mystery Dungeon" returns. That was quick.
In "The Great Bird Man," Xergiok returns.
"Simon and Marcy" continues the "Ice King's and Marceline's past" arc.
The episode "Puhoy" starts out with Finn and Jake stuck in the house because of a knife storm.
Jake's children are mentioned again.
Pillow Dad!Finn has the pillow equivalent of a mechanical arm, like all his other alternate selves except for Fionna.
At the end of season 4 in "The Lich", Booko explains that there exists a multiverse in which universes are randomly connected with naturally occurring worm holes or artificial worm holes created by a powerful artifact—like the Enchiridion. The pillowverse in this episode may be a nod back to that.
At the end of "Princess Potluck," it is revealed that the one shooting arrows at Jake was the squirrel from the season 1 episode "The Duke."
This episode also seems to take place during "BMO Noire," since Jake has his makeup on, and when the two return at the end of episode, Jake has an arrow in his head and Finn has the sea slug.
The Party God from season 2 episode "Party Animal" shows up at the end of "Shh."
He also plays a big role in "Party's Over, Isla De Senorita".
The Guardian Angel shows up again in "The Suitor", attending Peppermint Butler's demon summoning.
Tiffany shows back up again in "One Last Job", as does Jake Jr. Also, many of the random names on Jake's contact list in "My Two Favorite People" show up as members of his old gang.
"Wizards Only Fools" is full of these. Wizard City, its confusing signs, Abracadaniel, and Buffo, Forest Wizard, and Lazer Wizard's plot all return.
"Jake Suit" ends with the clown nurses.
Finn's "Puncha Yo Buns" dance returns as well, as does the "Jake Suit" from the goblin king episode.
The squirrel from "Up a Tree" flies by the treehouse on Finn's flying disk at one point.
"Sky Witch" is all about Marceline trying to get Hambo back from the witch Ash sold him to, mentioned in "Memory of a Memory."
The shirt Marcy gave PB from "What Was Missing?" also becomes a key plot point.
In "Too Old," Finn and Flame Princess are still broken up due to the events of "Fire & Frost." Also, the Lemon Children first seen in "All Your Fault" are shown to have grown up, and Lemongrab 2 is shown to be alive, albeit disfigured, after the events of "Another Five Short Graybles." This episode also displays several allusions to "Too Young," including the Lemon People having their own versions of Manfried and Cinnamon Bun, as well as Finn suggesting that he and Princess Bubblegum prank Lemongrab "like old times." Lemongrab's dungeon obsession returns again, as well.
Also Finn's flute, you know, the one he tried to use to fix a sad ogre's heart, makes a return.
Princess Bubblegum's passport has her first name on it, Bonnibel.
"Earth & Water" is can be considered a part three to the "arc" started by "Frost & Fire" and continued with "Too Old." Princess Bubblegum works on stabilizing Flame Princess's matrix after observing her destroy the Ice Kingdom. FP's matrix was first mentioned by PB in "Burning Low."
Ice King must stay at the tree fort due to the Ice Kingdom's destruction.
Ice King reminds Jake that they were both married to each other once. This happened all the way back in season 1, in the episode "When Wedding Bells Thaw."
In "Time Sandwich", Jake uses the pickles he got from Prismo at the season's start as part of his sandwich.
In "The Vault" we get to see when PB was dating Mr. Creampuff, that they dated was mentioned in the first episode ("Slumber Party Panic").
Once more, we see an alternate version of Finn with a prosthetic right arm.
Shoko's ghost first appeared in "The Creeps", and again in "King Worm". Finn's mental vault is also mentioned in those episodes.
Finn and Jake host a radio show talking about Finn's breaking up with Flame Princess (from "Earth & Water"). note Finn insists that they should stop talking about relationships and focus their efforts on adventure (which implies they stopped in the past... which is true). Finn's soreness over the break-up is a main source of conflict in the episode.
Ice King still seems to be living in the tree fort due to the destruction of the Ice Kingdom in "Fire & Frost." He started living there in "Earth & Water."
Slime Princess references "Prisoners of Love" by saying she used to crush on Finn.
In "Dungeon Train," Jake asks Finn if he's still sad about the break-up.
In "Red Starved" Marcy makes good on her song from "What Was Missing" and drinks the red from Bonnie's pretty pink face.
In "We Fixed a Truck," the Banana Man from "The New Frontier" returns.
And Ice King is still living in the tree fort.
"Play Date" revolves around Ice King overstaying his welcome at the tree fort, and Finn and Jake calling in Abracadaniel to convince him to leave. Ice King even mentions Abracadaniel beating him in "Wizard Battle."
Also, the demon Keeoth returns after IK and Daniel mess around with Joshua's demon blood sword.
The zombies from "Simon and Marcy" return in "James" after the crew find them in a pit in the desert.
Surprisingly enough, the ogre from "The Enchiridion!" ("I think your dog finally fell into my stomach!") makes a return in the beginning of "Root Beer Guy."
"Apple Wedding" is all about Tree Trunks finally getting married to Mr. Pig, which they mentioned they weren't ready for yet in "Dream of Love."
Jake and Lady's pups also have cameos in this episode. You can also see that Kim Kil Whan has a beard, just like Jake said he did at the end of "Jake the Dad," if you look closely enough.
"Blade of Grass" has a couple.
Finn mentions the female armor Choose Goose sold him in "Blood Under the Skin" when questioning whether to go to someone new for a sword.
When Finn and Jake visit Tree Trunks, she very visibly has her new wedding ring on after getting married to Mr. Pig in "Apple Wedding."
Finn still has his new grass sword in "Rattle Balls," but that isn't too surprising.
Root Beer Guy is shown to be the captain of the Banana Guards, the position he was appointed at the end of his titular episode.
Finn mentions his breaking up with Flame Princess to Princess Bubblegum and he shows his developed resistance to pain from fire injuries.
"The Red Throne" is essentially a continuation of "Earth and Water," since it deals with Flame King trying to usurp Flame Princess as the ruler of the Fire Kingdom. Cinnamon Bun is even a major character as he works for Flame Princess now.
The fire pup that Flame Princess gave Cinnamon Bun grew up rather quickly; it's able to hold three people on its back now.
"Betty" once again continues the Simon arc, revealing what exactly happened to Betty when Simon put the crown on.
The entire episode happened because we finally learned Buffo, Forrest Wizard, and Lazer Wizard's plans.
"Billy's Bucket List" has quite a few:
As to be expected from the title, this episode deals with Finn feeling guilty for Billy's death in "The Lich" so he decides to complete his bucket list for him.
One of the items on Billy's list is to lie face up in the ocean for a while, so Finn has to deal with his fear of the ocean as well as the Fear Feaster again. He conquers both.
He also manages to get into the ocean the same way he did last time: by knocking himself out.
The Party Bears, as well as the monster they reside in from "Belly of the Beast" return early in the episode.
Finn cuts the Fairy King's pants down, a technique we saw him practicing in "Rattleballs".
The remains of the Gauntlet Dock from "Business Time" appear in this episode.
In the episode “The Creeps” in order to make sure Jake is not possessed, Finn asks Jake to tell him who always stands next to him in his recurring elevator dreams. Jake responds correctly with “a half-orc shaman.” Nearly three years later, in the video game Explore the Dungeon Because I Don’t Know! Finn’s starting imagination attack shows him in an elevator with… a half-orc shaman.
You have to really be looking for it to notice on a first time viewing but in "Escape From The Citadel", Martin looks just like a mutated version of Farmworld Finn's dad; just as he should since he's an alternate version of that person. That's an absurd level of detail given that Farmworld Finn's dad only appeared for, at best, 30 seconds and had no dialogue.
Listen closely while Finn's psychic arm starts building the tower in "The Tower." He ponders whether he should go to Banana Man to help him build a space ship to help find his dad.
The Ancient Psychic Tandem War Elephant finally returns in "Furniture and Meat". Turns out he was "chilling" under all the gold in the treasure room under Finn and Jake's orders.
A shit ton in "Something Big."
The episode centers around Maja, from the titular "Sky Witch," finally putting her plan into motion.
The Ancient Psychic Tandem War Elephant returns again to fight the colossus, Darren.
Princess Bubblegum uses her laser swan from "Dungeon" to fight off Darren for a while.
Root Beer Guy came Back for the Dead when we learn that he died helping set up Gridface Princess' force field.
All the puppies finally make a proper return in "Ocarina," though most of them seem to resent Jake for never visiting.
Spending all of their treasure in "Furniture and Meat" ends up biting the guys in the ass when they don't have enough money to buy back the tree fort from Kim Kil Whan.