It's unknown what the title is a parody of, as there's various meanings to it's name.
During the boy band concert, the phrase "Yvan Eht Nioj" appears on the giant screen. It also shows it's meaning (Join The Navy) and is corrected back to the original phrase seconds later. A reference to the episode "New Kids on the Blecch".
The couch gag is a reference to the 2014 Disney short film, Feast.
During the credits, Homer mentions the movie Back to the Future when saying goodbye to the things at the island.
The Australian boy band seems to be inspired by the Australian pop/punk band Five Seconds of Summer.
Harper's father mentions that Jambowski island was formerly Haiti.
Lisa says that she has to pedal backwards to go forwards on her bike, but in every other episode where she uses her bike, the pedals work normally.
When Homer, Marge and Bart are preparing for the trip, Bart is flipping a flaming stick with a brown shirt. But when Lisa comes in, Bart's shirt turns blue.
Lisa and Harper are both barefoot when they arrive at the beach but when Homer chooses Lisa over the island, Lisa is wearing flip-flops. Also when Homer and Mike start fighting, Harper is wearing flip-flops, too.
Milhouse wouldn't be able to take Harper's bike to himself. The bike is equipped with a modern anti-theft device, so mounting the bike would draw Chief Wiggum's attention and possibly get him arrested.