Ear Worm: "Hey, hey! Life in the dreamhouse! Oh, yeah! Life in the dreamhouse!"
"Everybody needs a Ken, now and then, to hold onto!"
Einstein Sue: Grace didn't seem to have much personality beyond loving math and science. Since this apparently limited her comedic potential, she inexplicably disappeared after her second appearance.
Ensemble Darkhorse: The Schlond Poofa. Mattel took notice, and now has it cameo in various episodes. They also introduced such offshoot products as the Shnoggin Wrench and the Gold Schlond Poofa.
Foe Yay: Raquelle and Barbie, at least on Raquelle's end. She constantly tries to upstage Barbie to the point of obsession, and you could argue that the only reason she wants Ken is because Barbie has him.
Harsher in Hindsight: Grace's first episode, "New Girl in Town", ends with Barbie telling the viewers, "You can never have too many friends! It's science!" The writers must have realized otherwise, or else Grace would have had more than two episodes.
Moral Event Horizon: Crossed in "Gone Glitter Gone" after Barbie's sisters, Raquelle, and Ryan decide to tear Tawny open to get back the glitter she ate. Barbie calls everyone out on this.
No Yay: A few Dreamhousers object to Midge and Ryan becoming a couple, since Happy Family Midge had a son named Ryan.
Periphery Demographic: Due to it's somewhat self-aware nature and good jokes, this show has managed to get an audience outside of little girls. "The Ken Den" was Mattel practically admitting that they're aware men are watching this series.
What an Idiot: Ryan has the candy shop make a chocolate sculpture of him as a present for Barbie. When he shows it to her, he doesn't bring any shade for it. Barbie tries to remind him not to leave chocolate out in the Malibu sun, but the sculpture instantly melts before Ryan can move it.
The TV specials
Idiot Plot: "Trapped in the Dreamhouse" would've gotten resolved a lot sooner if Barbie remembered where Ken put the "evil" switch (he even showed her in "Closet Princess 2.0"), and flipped it back to its default setting.