Squidward is called Wolfgang Amadeus Tentacles in his dream.
In "Sandy's Rocket", SpongeBob declares, "You got your toothpaste in my peanut butter!" This references classic 1970s and 1980s Reese's cup commercials (where the characters would say "You got your chocolate in my peanut butter!" as well as the inverse).
The episode features a song called "Give Jellyfish Fields A Chance", which is a parody of John Lennon's "Give Peace A Chance". The scene that the song plays over is a parody of the music video for "Subterranean Homesick Blues".
The middle of the jellyfishing song has a slight rewrite of The Toyes' "Smoke Two Joints" (replace "two joints" with "jellyfishing").
Mr Krabs: There are 13 bad words you should never use. Squidward: Don't you mean there're only seven? Mr Krabs: Not if you're a sailor. (chuckles)
In "Christmas Who?", when Squidward (dressed as Santa Claus) asks a little girl what she wants for Christmas, she replies "Front teeth." This is a reference to the 1948 song "All I Want for Christmas Is My Two Front Teeth" by Donald Yetter Gardner.
In "New Student Starfish", Patrick's climb up the mountain of light bulbs has a brief shout out to The Price Is Right's Cliff Hanger Game, complete with yodeling and lederhosen.
"Karate Island" is one long shout out to Game of Death, complete with Sandy wearing the famous yellow tracksuit Bruce Lee wore in said movie.
The second half of "Squeaky Boots" parodies Poe's "The Tell-Tale Heart", where Mr. Krabs steals the rubber boots he gave to Spongebob and hides them under the floorboards of the Krusty Krab, only to still be driven mad by the squeaking.
In "Fear of a Krabby Patty":
The Giant Krabby Patty tells Spongebob, "I'll always be with you right here", while pointing to the protagonist's chest with a glowing finger, a reference to E.T.'s last words to Elliott in E.T. the Extra-Terrestrial.
The word association exercise between Plankton and SpongeBob references the famous line of the song "Let's Call The Whole Thing Off" from Shall We Dance? that named You Say Tomato.
"SpongeBob B.C." has the weird chanting and famous music from 2001: A Space Odyssey when prehistoric SpongeBob discovers that he can use fire to cook food.
Another reference to 2001 occurs in the episode "Sandy's Rocket", where a copy of the novel version can be seen floating in the rocket as Spongebob and Patrick briefly travel through space. The famous music happens to be playing during this scene too.
"Krabs vs. Plankton": When Plankton enters the courtroom, the theme from The People's Court plays.
After getting introduced to Patchy the Pirate, Robin Williams asks "There isn't someone dressed up as Popeye is there?" Doubles as an Actor Allusion, as Robin Williams played the titular character in the 1980 live-action adaptation.
At one point, Robin Williams says, "This is like a shot from the Raging Bull."
Robin Williams mentions the film Hook, in which he also starred.
The song "Oh, Krusty Krab" is a parody of "Oh, Christmas Tree".
Patchy ending up in the belly of a whale is a reference to Pinocchio.
"Big Pink Loser" has a shout-out to The Adventures of Buckaroo Banzai Across the 8th Dimension, of all things, when Patrick claims that his life's dream is "to defeat the giant Monkey Man and save the ninth dimension", later amending it to "to defeat the little Monkey Man and save the eighth dimension" when SpongeBob convinces him that it might be too hard. The titular "eighth dimension" was a key part of the plot of Buckaroo Banzai, and it also featured a race of villainous aliens who called all humans "Monkey Boy" ("It's not my goddamn planet! Understand, Monkey Boy?").
In "A Pal For Gary":
The premise of Puffy Fluffy being bought from a gypsy and becoming a monster overnight is modeled after the plot of Gremlins, where an adorable creature becomes a ravaging beast if fed after midnight. Only in this plot, the buyer ignores the seller.
In said episode, we see that Spongebob has a collection of books by T.S. Halibut, which is a parody of T.S. Eliot.
The episode has numerous references to Jaws, including the famous theme. The title card is also a parody of the film's iconic poster, with a dollar bill and a giant clam replacing the woman and the shark, respectively.
There's a reference to Moby-Dick, when Mr. Krabs nails a sandwich to the boat's flagpole as a reward.
There's another Jaws reference in "SpongeBob, Sandy, and the Worm," where the citizens are discussing what to do about the titular worm, when an old man who resembles a sailor scratches the wall in the same way the man in that film scratched the chalkboard to get everyone's attention. However, he just wanted to know where the bathroom was.
In "Ditchin'", the new Mermaid Man and Barnacle Boy comic book includes a panel about their origin story, which has their parents launching them in a rocket, just like how Superman arrived on Earth.
Using "Because they're so darn stupid" as the punchline to a lightbulb joke like SpongeBob does in "Squirrel Jokes" was previously done in Raising Arizona.
At the end of "SpongeHenge", SpongeBob sees the Krusty Krab abandoned and half-buried in the sand and breaks down, a la the ending of Planet of the Apes (1968). His hair and beard make him look like Charlton Heston as well.
To Larry "Lonesome" Rhodes' speech in A Face in the Crowd in "Chum Bucket Supreme", when Patrick resigns from slogan writing because his brain is burned out and Plankton boasts about the customers' gullibility:
Patrick: Anyway, you can send my check to my home. Plankton [unaware that his words are being broadcast over the loudspeaker]: Check? You want money for those stupid catchphrases? Anybody can sell to my idiot customers! They're buffoons, morons! They'll buy anything I sell them! They're the dumbest of the dumb, the stupidest of the stupid! They're dummies, dweebs, and doo-doo dunderheads. I can keep that rabble right where I want them! Huh? [A bunch of hockey players gang up against Plankton, and start hitting him with their hockey sticks]
In "Fiasco!" Plankton ducks inside a movie theater to evade the cops for stealing a priceless art piece made out of a krabby patty. The movie shown is blatantly The Blue Lagoon complete with the two teen characters about to kiss.
"No Pictures Please" opens with "The Tidal Zone", a reference to the The Twilight Zone (1959). It returns at the end after the tourist is revealed to have never existed in the first place. "The Night Patty" also ends with all the weird events that occurred being the Tidal Zone's doing.
"Feral Friends" features a green orb rising from a volcano and mutating everybody except Sandy into more savage, animalistic versions of themselves. It even has musical themes similar to the orchestral score in Heavy Metal.
In "Dying For Pie", Squidward briefly channels Ralph Kramden on the line "He's gonna drown in it! DROWN in it!" recalling Ralph's famous line to his mother-in-law, "YOU are a blabbermouth. A BLABBERMOUTH!"