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Raquelle accidentally refers to Chelsea as "Kelly", a shout out to the original name that character had in The Nineties and the Turn of the Millennium before being rebranded/renamed.
After meeting Grace, Barbie proclaims, "She is so in style!", name-dropping the doll line that introduced Grace.
Other Outside References
As mentioned on the main trope page, Raquelle's slow-motion run in "A Day at the Beach" has music evoking that played during the opening of Chariots of Fire.
Raquelle's boutique features prominently a Sistine Steal of The Creation of Adam, with Ryan taking the place of both God and Adam.
"Closet Princess 2.0" borrows heavily from 2001: A Space Odyssey, most notably through Barbie having a Cyber Cyclops that refuses to let her go outside, as well as a topiary of cavemen beating a monolith.
"Occupational Hazards" also features music similar to "Also Sprach Zarathustra" and a close-up of Ken's head in a space helmet while flashing lights fly by.
Raquelle quotes Jaws in "Accidentally on Porpoise" to explain her fear of dolphins.
Part one of "Gone Glitter Gone" has Stacie hiss, "Chelsea, give us the precious!" in a manner similar to Gollum from The Lord of the Rings.
Part two of "Gone Glitter Gone" evokes The Godfather as Chelsea implores Skipper, "Make me an offer I can't refuse." Also, Skipper gives Chelsea the severed head of a plush horse, offering to trade the whole horse for the glitter jar.
"The Ken Den" features gigantic barbecue ribs as well as a parody of the famous "dogs playing poker" painting.
The TV Special episode "Trapped in the Dreamhouse" reveals that the Dreamhouse has a Raiders of the Lost Ark-styled booby trap as well as a staff-and-gem-using locator and a thermal exhaust port weakspot. In addition, when Barbie has to take things out of her handbag so that it'll be the same weight as the thing she wants to remove from the booby trap, one of the things she takes out is a standard lamp.