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.
Homer refers to a sumo wrestler as "Baby Huey."
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"
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.
Homer quotes the line "Hasta la vista, baby"
The Americatown restaurant has an animatronic E.T.
Mentioned by name
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!"
Referenced by Woody Allen in his TV commercial
The pilot makes a reference to Gamera.
The pilot mentions Gidrah, the giant monster villain in this film.
The pilot makes mention of Mothra, the giant monster villain in this film.
The pilot references Rodan, the flying monster from this film.
The Americatown restaurant has an animatronic Marilyn Monroe in a white dress, which is being blown upward by a subway vent.
Godzilla attacks the plane in Japan, the pilot apologizes for "mild godzilla turbulence"
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.