This episode is part of a nice symbolism in the progression of the Gizmoduck arc. The first episode (The Great Dime Chase!) isn't about Gizmoduck per se, but about the idea of what could be. In that episode, Louie is the triplet point of view, as he confuses Lil' Bulb searching for the dime, creating a mad robot who Gyro eventually had to reign in. Gyro then uses the train of thought to better control his robots, by becoming a robot. Hence, Project Blatherskite. In Beware the B.U.D.D.Y System!, we see Fenton, the man who would take over the suit. That episode not only established the name, but also was about being willing to take a leap into danger to do the right thing. Fittingly, Dewey is the focus triplet for this episode, with him encouraging Launchpad to take a leap of faith; Launchpad then encourages Fenton to do the same, setting the idea of Gizmoduck in motion. Finally, this episode is about the responsibility and self-determination Fenton needed to make Gizmoduck the best hero possible; hence, he's paired up with the third triplet, responsible and erudite Huey.
After the events of "Day of the Only Child!", it makes sense why Bigtime Beagle recognizes Huey by name: he was the one that Burger and Bouncer teamed up with during the Junior Woodchuck cooking contest and the one who got Bigtime's brothers to turn on him. Bigtime has a pretty big reason to have a personal grudge against Huey, so of course he would remember his name.
At first it seems like Mark Beaks has been given the Karma Houdini treatment once again, as he's never shown answering for his misdeeds throughout the episode (although he does lose the Gizmosuit and have his office wrecked). But if you think about it, the disaster he caused with the unstable Gizmosuit at his press conference was the worst possible thing that could've happened to him. As established in previous episodes, Mark clearly values his reputation over his wealth, and if his actions at the press conference are anything to judge by (trying to pass himself off as Gizmoduck the whole time only to be called out immediately on the lie, saying he'll only save those who can afford it, and putting innocent people in danger with his bungling with the Gizmosuit), his public image has taken major damage, which is just the kind of thing an Attention Whore like Beaks wouldn't be able to stand.
Mama Cabrera's Adaptational Badass makes perfect sense when you realize that she and her son had their roles reversed at first in the series. Namely, that Mama is the breadwinner for the house because Fenton had taken an unpaid internship. Ergo, her work in the law.
Mark Beaks expresses casual racism when he addresses Fenton and only Fenton, who is their world's version of Cuban, as "amigo" and "chico". This works with him being a parrot: he's repeating terms he's heard from others without thinking about whether they're appropriate.
The reason Mark Beaks and Huey are able to respectively hack and rewire Gizmoduck probably goes back to Fenton releasing Gyro's plans on the internet.
Beaks' apparently unwarranted confidence in operating the armor comes from him understanding the Lil' Bulb-era tech - which didn't have any of the complicated devices and control systems that Gizmoduck has. (Conversely, if the Gizmoduck armor was only as complicated as Lil' Bulb's Money Sorter armor from "The Great Dime Chase!", he'd probably have been more successful. Missed shout-out to Iron Monger, really; more's the pity.)
Huey's solution to completely bypass the control system(s) with wetware, and also rip out the processor core, comes from the same - except he actually understands the tech involved beyond just what's necessary to duplicate it. It's also the difference between him and Gyro: he trusts the duck inside and Gyro can't.
Beaks, amusingly, may have been using Waddleduck the way Gyro actually intended it: not as a hero but as a general all-purpose robot.
