Achievements in Ignorance: Dave, who can fix anything. At the very beginning of the strip, he is able to reconstruct a fully functioning weather-control device from a broken mail sorter that Helen tricked him into believing was a broken mail-order doomsday device. The resulting device can control pre-existing Kill Sats.
Subversion too, as he's really a latent genius.
Affably Evil: Helen and Mell do pretty unpleasant, not to mention unethical and irresponsible, things pretty much constantly. But they're so darn charming its easy to forget.
Helen: You are Dave Davenport. You've fought demons, flown to the moon, came back from the dead, and menstruated. I've put you through much worse than this.
Art Shift: Every year has a Dave-in-Slumberland strip whose art style is based on that of Little Nemo and Dreams of the Rarbrit Fiend. These contain coded clues for what will happen in the following year of strips.
Awesome, yet Impractical: The bane of most mad scientists. The dangerously sane (by Narbonic standards) Mell lampshades this when she draws an analogy between a highly advanced but thoroughly impractical laser flintlock pistol designed by Madblood to mad science in general.
Mell: What's awesome is, this gun is like you! It's mind-blowingly brilliant, but on a common-sense level it's dumb as a box of rocks! And in the end it blows up in your face. Big surprise, huh?
Dave Davenport: Here's the situation: Right now, you need a mad-scientist liaison. I'm a mad scientist. You're going to hire me. Dave Conspiracy: And what will you do if we refuse? Dave Davenport: You know, I have no idea. [twitch]
Bad Future: Dave ends up in one when he's unstuck in time. One of the residents there, a holographic recording of Dave (or possibly a version of Dave's mind that's been uploaded into the computer), gives him a subtle clue about how to fix the future.
Briar Patching: Confessed by Dave here: "If that's the way they want it, I'll just have to cope with living on a tropical island with two scantily-clad women." (Also a heavy dose of Foreshadowing and or Fridge Brilliance on the part of the author.)
Bold Inflation: Two plus two words: ANTONIO SMITH (FORENSIC LINGUIST).
He would kill you for writing his name in all caps.
Unless he's wearing the fedora.
Broken Faceplate: The state of Dave's eyeglasses symbolizes the state of his sanity. For most of the comic's run, his glasses are intact but represented as opaque. Towards the end when Dave finally realizes the great secret responsible for much of his life's path, his glasses are suddenly represented as clear, showing that he can see clearly now. And then one of the lenses cracks, as a not-so-subtle way to show that Dave is half-cracked.
Butt Monkey: Madblood and Dave for much of the comic. They still don't have anything on Victorian Madblood, who ended up the sole consort of a planet of shapeshifters who decided they all liked his form best.
Buxom Is Better: Mell acknowledges the assets of the Avatar of Lovelace, Madbloods A.I.
Brain Bleach: Mel's reaction to Dave's clone having found erotic photos of Dave and Helen B. together: "MY EYES! MY EYYYES!!" (warning, spoiler)
Cloning Blues: Helen was scarred by growing as the subject of experimentation by her mother on the heritability of Mad Genius, and worries that she's turning out just as bad. These worries become especially relevant both in her experiments on Dave's nascent madness and her bringing out a clone of Dave after their breakup. The Dave clone is killed by Dave as part of his Villainous Breakdown.
Drunk on Milk: Dave can get stone drunk on half a glass of Vanilla Coke. (And pathos.)
Dude, Not Funny!: Helen B.'s reaction to Artie joking about how Dave was either eaten by a demon or forgot about the date with her. She found the latter much less funny then the former. (click with caution, spoiler!) invoked
Easter Egg: A story of Helen's origin can be found (two or three words at a time) attached to the filenames of the individual strips. The compiled story can be found here.
Elaborate Underground Base: played straight with Helen's lair, but subverted as well. Madblood brags about his "underground lair", but it's revealed that "underground" means "living in Mom's basement".
Helen's "underground lair" is actually a storm drain. They just do a really good job fixing it up.
Filk Song: This has become a running feature in the comments section of the "Director's Cut" re-runs. For example, this strip inspired one reader to compose "In The Dungeon We'll Rot" to the tune of "You're The One That I Want" from the movie version of "Grease".
Foreshadowing: Almost everything in the comic. Side characters, oddball filler arcs, offhand comments, almost everything comes into play later.
Floating Continent: The intelligent hamsters Dane, the superintelligent gerbil created, made a floating village with Artie's donation.
For Want of a Nail: "Listen, Dave. When the time comes, you must refill the swimming pool. Got it?"
Freak Out: All mad scientists go through this when they first go mad. Hellen's, told in an Easter Egg spanning literally the entire strip's run (hint: Look at the filenames of the strips) involved her turning a bunch of pasta into a deadly bioweapon.
Note that, of the scientists who mentioned the settings and casualties of their initial freakouts, Helens was the most destructive. The competition included a nuclear power station.
Dave's involves him taking over Madblood's evil lair, killing off the local advanced AI, and uploading his own brain to take its place.
In the Bad Future, he is strongly implied to have topped this off by successfully escaping the base and setting off a global thermonuclear war, after Helen is either badly injured or temporarily killed in her fall and is thus unable to distract him at a pivotal moment.
Generation Xerox: Not only is Helen a literal "xerox" of her mother, but her life and personal tastes parallel hers in several ways, occasionally to her angst.
The Victorian Narbonic storyline may or may not be part of canon, but there are at least two ghosts to testify to a Helen, Mell, and Dave living over a century ago having similar mad science adventures.
Good Angel, Bad Angel: Played with — not only is there Good Angel, Bad Angel, but there's "Social Life", "Mad Scientist", "Self Esteem", "Fear of Women", "Biological Clock"... And the characters can all see their own, and the angels can see each other — and socialize after work.
Gratuitous Italian: The Italian spoken by the Amazon Women of Mars in the Victorian storyline oscillates between nearly normal and positively Jabberwockish.
Heartbreak and Ice Cream: After Helen breaks up with Dave, she expressed her intent to eat six pints (2.84 liter) of Ben and Jerry's "Half Baked" ice cream. Since she's a mad scientist, she also wants to blow up Ecuador.
Hey, It's That Guy!: Shaenon Garrity litters the Mad Symposium of "Professor Madblood and the Lovelace Affair" with cameos of mad scientists from other webcomics.
Also the physicist and the webcomic artist who Artie meets at the dinner? Ink Suit Actors of Paradigm Shift creator Dirk Tiede and his future wife.
Informed Ability: Dr. Narbon's only major scientific accomplishment (mad or otherwise) is her longitudinal study of her daughter-clone Helen Beta. Everything else, she snitches off Helen's work. This is brought up a few times, naturally. She's pretty good at the Evil Overlord gig though.
Kinetic Weapons Are Just Better: As Mell points out, Madblood has armed his robots with laser weapons that expend a rare moon crystal for power...which get one shot per crystal and must be manually reloaded like an antique pistol.
My Little Panzer: In "A Week of December 18th Story", a parody of A Christmas Story, little (future Mad Scientist) Helen's Christmas toy of choice is the BioBeam 8000 gamma irradiator with 5-liter containment chamber, cesium 137 radiation source, optional remote monitoring station, and a thing on top that tells the time. This is apparently a real piece of equipment.
Morality Chain: After Helen B. broke up with Dave, Mell claimed, that Dave made her act more sane.
Naked on Arrival: When you get kicked out of the afterlife into the mortal world, you're naked. Happens to both Caliban and Mell.
Dr. Fowler: "Yes, that was simply a killer pesto wasn't it, Narbon?"
If one reads the side story, added a word or two a day in the filenames, the tale of that Italian Bistro is told.
Not So Different: Poor Artie causes a lot of chaos, despite being the token good member of the cast.
Not-So-Harmless Villain: Helen comes across as a slightly goofy, hopelessly inept mad scientist playing to all the tropes (and a Hollywood Nerd). Turns out this is a persona she wears at all times to be able to interact with people on our level. When she has to go up against another newly-gone-mad mad scientist, she warns the rest of the cast that she will be too busy to play nice.
Artie: So what we've seen up to now is the reassuring persona?
Mel: Hells yeah. Not even I wanna meet Real Helen in a dark alley.
Running Gag: After Dave's smoking was wiped out of existence by time-shenanigans, "Dave never smoked" became a running gag in the comic, Director's cut commentary, and fandom.
Sanity Has Advantages: Played with. One girl who's been seen in the bar Dave frequents comments that the first time she met him, he was driving androids to Canada, and the second time he was licking the barroom floor.
Dave: "So sanity's not coming off too well?"
Girl: "I'm just not seeing much of a difference, is all."
Scary Shiny Glasses: Dave is an odd example - his eyes are covered sporadically by his glasses throughout most of the comic and only go totally clear once he goes mad. The elder Doctor Narbon also wears glasses obscuring her eyes in all of her appearances in the comic except for when Dave meets her while traveling in time, where she looks exactly like present day Helen.
Science-Related Memetic Disorder: Mad genius is an actual genetic condition, and Helen manages to find a cure for it... but with the side effect of decreasing the subject's intelligence and amplifying their Weirdness Censor to an astonishing degree. (Helen also says she didn't use it on Dave because it makes the user impotent, but Word of God is that was a joke.)
Set Right What Once Went Wrong: Among other things, Dave quit smoking by never starting in the first place. In a more plot heavy moment Dave from the future specifically invokes this trope by leaving a holographic message to a time hopping Dave from the present that he's not happy with his life, and gives him instructions on how to fix things.
At a mad scientists' convention, a supercomputer is asked to sing 'Daisy, Daisy'. It refuses. It later takes an opportunity to say: "I'm sorry Dave, I can't do that." Later still, as it's being erased, the supercomputer says "Dave, stop. Stop, will you? Will you stop, Dave? I'm afraid. Dave, my mind is going. I can—"
Soap Punishment: Helen's mother punished her daughter for saying the "g-word" (No, she wasn't swearing in Russian or Polish, as a Card-Carrying Villain Helen senior finds the word "good" obscene and dirty).
Suicide Attack: The gerbils send the cat Sir Pounce, that Helen sent to keep them in check, as a suicide bomber against Helen. Mel tossed it away and it killed 3 of the gerbils.
The Walls Are Closing In: When Mell is sent on a mission to kill Dr. Narbon, she falls prey to this after commenting, "Huh, weird floor." Her captor comments that there wasn't time to come up with something original, since Mell made it farther than expected.
Wham Line: "How do you know I'm mad?" asked Alice. "You must be," said the Cat, "or you wouldn't have come here." And then Dave was a madboy.
Weird Trade Union: Both henchmen and killer androids have their own unions. (That last one was actually Artie's fault.)
Weirdness Censor: Dave's brother Bill is an extreme example — rather than merely reinterpreting weirdness as mundane things (for example, treating Artie as a normal gerbil) he does not perceive weird things at all (for example, he just can't see Artie).
When Helen tests her Science-Related Memetic Disorder antiserum on a clone of Dave, he gains one that's just as strong; someone even mistakes him for Bill for a moment or two.
With Great Power Comes Great Insanity: Mad scientists are utterly brilliant and can do things that should be impossible... but their genius is tied to their madness, which makes them volatile and destructive. It's probably also the reason that none of them has ever actually achieved World Domination.
Woobie, Destroyer of Worlds: Near the end of the comics, Dave goes mad and becomes a virtual virus that could infiltrate the world's technological grid and destroy the world.