The episode title is a reference to the chorus lyrics of the 1980 song "Refugee", by Tom Petty and the Heartbreakers, "You don't have to live like a refugee."
Ezra, the Stuffwich Sandwich spokesman, is a parody of Jared Fogle, who became famous for appearing in ads for Subway sandwiches until his arrest in 2015.
Nelson's speech mentions a man who "cut his foot off to save his family from Jigsaw." This is a reference to the character Dr. Lawrence Gordon from the movie Saw.
Martin and Lisa are presenting their speech on Marie Curie, the famous Nobel-prize-winner physicist and chemist.
The female figure Lisa thinks of is Margaret Mead, an American cultural anthropologist.
"La Marseillaise" is heard during Martin's speech of Marie Curie.
The magazine L'ESPN is a reference to ESPN, the sports channel.
The executive vice president of the World Football Federation is arrested for corruption. This is a reference to the FIFA football association, which was several times linked with corruption.
Homer thinks the best sporting event was the 2008 Super Bowl. This Super Bowl was ranked fifth on NFL.com's 100 Greatest Games, and is the highest ranked Super Bowl game. The new executive vice president remembered a pass made by MVP Eli Manning to David Tyree.
The TV series that the lady on the plane can watch on HBO include Hung, Bored to Death and Enlightened. These three have all premiered on HBO in real life.
Marge is using the app Tower of Babble to learn Portuguese. This is a parody of the language learning software Babbel, whose name is also a pun on the biblical Tower of Babel.
Homer mentions that Rio is the naughtiest city ever since San Francisco got all nerdy.
The app that Marge has on her tablet that is helping her with her Portuguese is called "Tower of Babble", possibly a reference to the Biblical story, Tower of Babel about how all of the different languages appeared in the world.
This is the second time that the Simpson family travels to Brazil. The first was in the episode "Blame It on Lisa" from Season 13, Tiago, the samba school teacher, reappears and once again calls Marge a "stupid lady". Xoxchitla also reappears and Bart watches her show.
This is also the second time that Homer Simpson is a referee in a soccer game. The first time was in the episode "Marge Gamer" from Season 18; the events from that episode are mentioned in Lisa's speech.
The music playing in the background when the Simpsons go out to eat (after the Brazil vs. Luxembourg soccer match) is the music from Teleboobies, when Bart watched the show during the family's first visit to Brazil.
In her speech, Lisa mentions Homer having once worked two jobs to get her a pony ("Lisa's Pony") and having bought her a saxophone ("Lisa's Sax").