The fish that Bart kills during his job in Osaka ("Spare my life and I will grant you three wishes") is a reference to the fable "The Fisherman and His Wife". Interestingly, when Homer was talking to Ned about how he thought they were, he states that he has Marge locked up in a pigsty, which is the same place the Fisherman and his wife reside in said fairytale.
When Marge says to Homer on the plane that she liked Rashomon (1950) by Akira Kurosawa, Homer claims he doesn't remember it that way. The underlying joke is that this famous film is about people remembering different things about the same event.
Battling Seizure Robots, the seizure-inducing television show that the Simpsons watch in their hotel room, is based on an episode of Pokémon called "Denno Senshi Porygon", which caused several hundred children to develop epileptic seizures. According to Mike Scully, the staff received "several angry letters" from people for the scene.
During the scene where Godzilla, Mothra, Rodan and Gamera appear, if you listen closely you can hear the roar of the monster Gabara, who made his only appearance in 1969's "Godzilla's Revenge" (a.k.a. All Monsters Attack). This suggests the monster audio for that scene was taken from that film.