At the end of Arthur's New Year's Eve, when Arthur remembers the different events of the past year, clips include he and his class laughing at the Rainbow Rock State Park dinosaur presentation (from Buster's Dino Dilemma), Arthur meeting up with Francine on their bikes, everyone dressed up for the Thomas Edison play (from Francine Frensky, Superstar), Arthur and his friends playing softball on Mr. Frensky's team (from Arthur Makes the Team), Binky, Francine and Muffy's mummy report gone wrong (from Team Trouble), and Arthur sledding with Buster and Francine (from Sue Ellen Moves In).
Binky reads the title card for "Arthur's First Sleepover". It's the one where Buster walks up to the circle and makes a noise. He burps in this title card.
Francine reads the title card for "Arthur's New Years Eve". It's the one where Pal chases a frog and D.W. shouts "Wait! Come back!" and both the frog and Pal return.
The ways Arthur's friends tell him that New Year's is ushered in is as follows -- Prunella says that there's a green flash, Francine says you must throw out your old calendars or being arrested by the New Year's police, Binky says there's a wrestling match between an old man wearing last year's date and a little kid and Buster says his cousin told him parents have a meeting conducted by aliens in they gather to talk about the awful things they did to their kids that year, and scheme up new ones.
This episode previously aired on New Year's Day or the first weekday after it on most PBS stations. As of at least 2006, the episode generally airs on New Year's Eve on most PBS stations.
(D.W. enters the backyard where Arthur, Buster, and the Brain are to have their sleepover)
Arthur: D.W., no! You aren't invited.
D.W.: Why not?
D.W.: Because why?
Arthur: Because, because.
D.W.: Because, because why?
Arthur: Because, because, because.
D.W.: Because, because, because WHY?!
Arthur: (slows down) Because, because, because, because...
(the Brain whispers into his ear)
Arthur: You'd get scared of the dark.
D.W.: No, I wouldn't.
Arthur: Yes, you would.
Brain: Who do you think's gonna win?
D.W.: (in Arthur's dream sequence) Arthur, Mom and Dad say you have to let me come to your sleepover!
Arthur: (wakes up and screams)
Mom: I knew he'd have nightmares with all this talk of spaceships.
Arthur: Happy New Year, Pal. And next year, we're going to see the green flash, and the wrestling, and the police...
D.W.: It was great! Big explosions and giant mules jumping off roofs into the ocean.
D.W.: Was that it? That was it!?
Grandma Thora: Yes, D.W. Happy New Year's.
D.W.: Hmph. What a gyp! I'm going to bed!
D.W.: I had a nightmare polar bears were chasing me around the North Pole.
Arthur: Bye. Have a nice meeting.
Mr. Read: Huh?
Arthur: Oh, I mean New Year's.
D.W.: I'm practicing ways to stay awake until midnight. Watch this one, ice! (slips an ice cube down her back) Eee, ooh, ah! (makes various grunting noises as she jumps around from the cold until the ice cube falls out and Pal eats it) Boy, that's brisk!
Arthur: (regarding New Year's) I'm too mature to care anymore.
D.W.: Yeah. Right. Mom, what does "mature" mean?
(Arthur and his friends realize that the "spaceship" they saw was actually a flashlight rigged by D.W.)
Arthur: I know where that "spaceship" came from... Planet D.W.!
D.W.: What if I'm trapped in some kind of time warp, and I'll never get any older. Is that my fault?
D.W.: Hey Arthur, guess what? I saw New Year's and you didn't. It was great!
"Arthur's First Sleepover" is based on a 1994 book by Marc Brown of the same title. Differences include a paper called "The National Requirer" (instead of "The National Observer"), the tent being much bigger, Arthur and his friends making signs to attract aliens, the kids getting a pizza delivery, and when D.W. shines the flashlight outside the window like spaceship headlights, Arthur, Buster and Brain panic and run off with the tent over their heads and crash into a tree (instead of the tent just collapsing on them), and the boys don't create a fake flying saucer like in the TV adaption.
During Buster's nightmare when he sees Arthur and The Brain as aliens, he does some rather cartoony takes (his jaw dropping to the ground, his eyes popping out and becoming gigantic, etc.) This mainly references the classic sight gags from the old Tex Avery cartoons of the 1940s and 1950s, as well as similar gags used on the Jim Carrey movie The Mask.