Furry Fandom: One villain is a massively obsessed animal activist who gives animals human intelligence and the ability to walk upright and speak to create a new species to overthrow the human race. At the end when defeated, as a last resort he splices himself with his pet wolf to try and fight back, but still loses. It never shows him change back after being arrested, though seeing the type of person he is he's probably happier being this way.
Gadgeteer Genius: Marc. In the first episode, he reprograms one of their gadgets in mid-mission in seconds.
Good Parents: Cal and Karen Clark. Heck; they're so much this trope that when it appeared that their parents had attacked their sub with intent to kill, Marc honestly believed his seasickness was making him hallucinate and the other 3 were in just about complete agreement. And for the record, they were right about their parents not wanting to hurt them. It was a ploy by Davey Hacker to get rid of the Clark kids by brainwashing their parents into doing his dirty work. And it almost worked...
Incest Subtext: Marc and Megan are awfully close with one another, often seen with one arm or shoulder around the other in screenshots, and Megan is always there to advise Marc on social graces. The subtext is subtle but definitely visible.
Shout-Out: Done very subtly in "Operation Grow Up". The episode features a villain that can alter his age at will, becoming a child at some points, an adult at some others, but one of his distinguishing traits is that he has a small scar on his chin at all times. Earlier in the episode, Tony is upset because he's too young to see a movie his older siblings are all going to. It isn't mentioned by name, but the poster the children bring back features a very familiar silhouette. Fans of the franchise need not hear more. Sneaky!
Marc's crush in "Operation Crabby Bob" is named Sheena Weston. Remind you of anyone?
Not to mention that Megan as Gravity Girl in "Operation Fun and Games" can easily remind one of Storm.
Sibling Protective Instinct: The Clarks may fight like cats and dogs and give each other a hard time but if you mess with one, the other 3 will mess you UP!
Super Mode: Happens to Lee, Marc, and Megan in "Operation Fun and Games"
Super Villain: The villains in this show, while they do still have really stupid Freudian Excuses, they're costumed and have powers or gadgets related to their "Theme", the the old show had some shades of it, but this show has more obvious Super Villain inspiration. Even the villains that do return from the original show have underwent a reworked design more befitting of a Super Villain.
Team Dad: Jerry naturally by virtue of being the only adult in on the spy gig but Lee will play this role to some degree when the kids are on their own.
Team Mom: Megan. While it's not constant, she does frequently go out of her way to help her little brothers.
Teen Superspy: Just Lee, technically. He's thirteen; his three siblings are a year younger (or two, in Tony's case).
In the second season he ups it up to fourteen while Marc and Megan become thirteen, thus counting as examples as well.
Tomboy: Megan, at least according to her brothers.
Transformation Sequence: If the way they put on their spy suits in every episode doesn't count (it's simpler than most examples, but still), then the time that Lee, Megan, and Marc turned into super heroes in "Operation Fun and Games" definitely does.
A Twinkle in the Sky: In "Operation: Twins of Trouble" a WOOHP jet does this as it flies off into the distance.
Unsound Effect: The opening sequence is full of them. It's used periodically within the episodes.
We Want Our Jerk Back: Tami becomes the Clarks' friend in "Twins of Trouble" after they save her life, and she ends up causing them more trouble in helping them than she does antagonizing them. Realizing that they liked Tami better before, they eventually let her "save" them so that the debt is paid and she can go back to being the Alpha Bitch.