Homer refers to a sumo wrestler as "Baby Huey."
When Homer complains that he would rather go to Jamaica than to Japan, Marge reminds him that "You liked _Rashomon_," to which Homer replies, "That's not how I remember it." This is an allusion to (and joke about) the way the various characters in Kurosawa's film have differing memories of the way the events in the central story transpired.
Godzilla attacks the plane in Japan, the pilot apologizes for "mild godzilla turbulence"
The Americatown restaurant has an animatronic Marilyn Monroe in a white dress, which is being blown upward by a subway vent.
The pilot references Rodan, the flying monster from this film.
The pilot makes mention of Mothra, the giant monster villain in this film.
The pilot mentions Gidrah, the giant monster villain in this film.
The pilot makes a reference to Gamera.
Referenced by Woody Allen in his TV commercial
The fictional movie which is being filmed in the plane where the Simpsons travel to Japan which features Jim Belushi dressed in a toga while screaming "TOGA!"
Mentioned by name
The Americatown restaurant has an animatronic E.T.
Homer quotes the line "Hasta la vista, baby"
Homer said that he would like to pilot a giant purple robot once he gets to Japan. Homer was referring to the Evangelion (mecha) from the popular anime Neon Genesis Evangelion.
Barney, while impersonating Homer, says "That boy ain't right", a line frequently used by Hank Hill.
The Simpsons family watches a Japanese cartoon called "Battling Seizure Robots". They then have seizures.
Characters watch a cartoon which causes siezures, a reference to the incident where an episode of Pokemon caused hundreds of siezures accross the country of Japan with flashing red eyes.
Jim Belushi is seen starring in a version of Animal House, proclaiming "Toga! 2000!" John Belushi starred in the original Blues Brothers, with Jim Belushi in Blues Brothers 2000. John Belushi also starred in the original Animal House, so this is implied to essentially be "Animal House 2000"
The cups in the 33 cent store read "That 70's Show"