Chalkboard: I will not carve gods

Couch Gag: The family rushes in and bounces to different spots.

The list of kids' names on the Krusty Show Birthday List:

Anna Goodwin
Reagan Gray
Paul Grenville
Jim Greigor
Harriet Hartman
Mike Himes
Julie Hirsh
Janet Hopkins
Cara Hunter
Gracie Jensen
Loretta Kangas
Marilyn Katz
Ken Keeler
John Lanzetta
Lorna Lefever
Marie Lichterman
Iris Lowe
Kim Madrigal
Cammie McGovern
Bill McLain
David Moulton
Mary Myron
Nigel Nelson
J. P. Patches
Ted Phillips
Randy Plot
Brady Reed
Kevin Reilly
Pete St. George
Casey Sanders
Matthew Schneider
Patrick Semple
Emma Shannon
Bart Simpson
Larry Stone
Beth Summerlin
Kate Sunberg
Dale Thomas
John Travis
Eric Van Buerden
Patric Verrone
Lee Wallace
Jay Weinstein
Chris White
Jay Wiviott
Henry Yeomans

Two of the names on the birthday list (Ken Keeler and Patric Verrone) are the names of two Simpson staff members who would later join the show.

Ken Keeler is the Simpsons writer who gained notoriety for penning the season nine episode "The Principal and the Pauper" (other episodes Keeler has written are "El Viaje Misterioso de Nuestro Jomer", "Brother from Another Series", and "Two Bad Neighbors").

Patric Verrone (credited as Patric M. Verrone) is (as of 2009) the head of the Writers Guild of America, Western Division. Verrone wrote for The Critic (which notoriously crossed over with The Simpsons in "A Star is Burns") and only penned one Simpsons episode: season 17's "Milhouse of Sand and Fog".

Wal-E-Weasel: Hey there, I hear it's your birthday, how old are you?
Bart: Well, I'm...
Wal-E-Weasel: That’s great! Would you like us to sing you a special song?
Bart: Hell no!
Wal-E-Weasel: You've got it, ready Señor P. Varotti?
P-Varotti: I'm-a- ready! And a one, and a two!
Song: You're the birthday, you're the birthday, you're the birthday boy or girl!

Bart: Look, I'll level with you; there is no Timmy 'O Toole, it was just a prank I was playing on everybody.
Lou: Well you sure fooled us, kid.
Eddie: Hey I've got an idea for a prank. Let’s go home and go to sleep. He-he-he.

(Volunteers offer to help Marge and Homer with Bart's predicament in the well.)
Falcon Man: Grasping the child firmly in his talons, Socrates here will fly him to safety! Just watch.
(The falcon is released and flies away) I don't think he's coming back.
Sea Captain: With this hook, and this hunk of chocolate, I'll land your boy. And I'll clean him for free.
Professor Frink: Although we can't reach the boy, we can freeze him with liquid nitrogen, so that future generations can rescue him.

Bart: Rod, Todd, this is God!
Rod: How did you get on the radio?
Bart: What do you mean “how did I get on the radio?” I created the universe, stupid kid.
Todd: Forgive my brother, we believe you!
Bart: Walk through the wall; I will remove it for you! (bumps) later…ha, ha, ha!

The sign at Wall-E-Weasel's says, "We cram fun down your throat."

The headline that the reporter is working on says "Town to Well: "No More Free Food'"

Jaws

One of the people offering to help pull "Timmy" out of the well is a fisherman similar to Quint, played by Robert Shaw in Jaws.

War of the Worlds

Bart pulls a prank by faking an alien invasion over the radio. This is a reference to Orson Welles' famous broadcast of the 30s.