Aborted Arc: Sierra spends the rest of season 1 and most of 2 trying to break Riley and Johnny up so Sierra can be with him. Yet after Johnny broke up with Riley, Sierra seems to have lost interest in him. Though she created a misunderstanding with Riley and Johnny's cousin.
Acme Products: It seems everything in the world is made or run by Fleemco.
Adults Are Useless: One of the driving points of the show as the adults the twins run into usually are quite ineffective in helping them, though more often then not the ones that do get replaced turn out being much worse.
All There in the Manual: The timeline on the official Fleemco website revealed that the company's previous owner was Conrad's brother Chauncey, a stubborn man who refused to listen to other people or try to understand them, nearly running the company into the ground as a result (he supported Betamax, for crying out loud). Conrad inherited the company after Chauncey disappeared during an ill-advised rafting expedition. This explains how Todd and Riley wound up in the orphanage, and why Conrad wanted to teach them about understanding other people before revealing their heritage and birthright.
Be Yourself: When Riley becomes the coolest person in school, she quickly becomes sick of everybody copying her. She delivers a big speech to the school about how everybody should stop mindlessly following trends and trying to be whatever some magazine says is cool right now, they have the freedom to choose for themselves. Quickly turned into a Spoof Aesop when Sierra replies that mindlessly following trends is what they chose to do and Riley has no right to try and stop them. Riley can't think of a rebuttal for that and gives up.
Four-Fingered Hands: This was true for the earlier seasons, but later they all acquired five fingers.
Getting Crap Past the Radar: Many examples. One of the more obvious examples was in the episode where Fleemco turned out to be developing an anatomically-correct robotic duplicate of underage Riley. Part of her assembly was shown, with scientists gawking at the double's naked leg in a scene which strongly implies that the rest of the robot was also naked.
Then there's the episode where Abby's sister basically treated Todd like a gigolo, showering him with gifts in return for dating her
In the "Freaky Friday" Flip sideplot of an episode when Dick in K's body drives C.A.R, he was highly disturbed to find out that he was being driven by Dick the whole time and tells in horror the details with what he had allowed him to do. To that end, he gives himself a traumatized wash down while saying he'll "never get clean".
Genre Savvy: Garth the janitor is downright obnoxious about this in one episode. He refuses to help Riley because "every time i slightly inconvenience you or your funny-looking brother, some guys in jumpsuits show up and send me somewhere nice for a few weeks." When said jumpsuits turn up, he's waiting impatiently for them with his suitcase already packed.
Irony: Riley uses a cute lifeguard to make an unnoticed Johnny jealous, much to her frustration. Then Riley unintentionally broke the lifeguard's heart because he developed feelings for her. As a result, the pool was closed, which causes everyone to hate her, including Johnny who was about to ask her out.
Kissing In A Tree: The episode where Riley tries to find a girlfriend for Shelton has Sierra not only tease her with this song, but Todd actually visualizes it. Also, Jacobo and Tasumi state that they were actually doing this in the last episode.
Nervous Wreck: In "The Truth Hurts", the head of the school newspaper who is replaced is a Nervous Wreck who is constantly jittery and gets extremely nervous about the idea of anything being published in the school newspaper that would make things like fruit on the bottom yogurt as opposed to being like plain yogurt, as he likes it.
Never My Fault: She doesn't even apologize to Johnny for her yandere-ish behavior.
No Celebrities Were Harmed: Sheldon again; he has Jerry Lewis' voice and mannerisms. Also, a sleezy salesman does a fairly good Phil Hartman.
Power of Love: Made fun of in 'German Squirmin': Sheldon: "Princess Cuddlepuff wields the power of love... which apparently wasn't powerful enough to defeat his doom ray...
Retroactive Wish: In one episode, Todd had the school librarian replaced with someone who'd turn the library into a place where he'd like to be. Riley got ran over by a buffalo stampede right after she asked if they were what'd come next. She asked about a unicorn stampede but nothing happened. She complained because it worked with the buffaloes, causing another stampede.
Running Gag: Several, notably that whenever Tasumi gets mad with someone, she puts them on her "list" of enemies (a series of Kaiju-type monsters). If you really anger her, you go above Gamozaur.
Will They or Won't They?: Riley and Johnny, as of season 2. Riley still has feelings for her and tries to get him back, but her Yandere-ish nature ruins it. At the end of one episode, Johnny may want to get back with her, but Riley wasn't interested.