Per Jeph, one of the biggest influences on QC is Azumanga Daioh. It's not hard to see some of the parallels. He also reads a lot of Yotsuba&! which is by the same author - Marigold even has a poster of her in her bedroom.
Anything That Moves / Depraved Bisexual: Pintsize zig-zags both of these repeatedly. He flirts with/harasses women throughout the comic, steals Faye's underwear, and compliments random women on their breasts, but he has had at least one relationship with another male. Since it was a male robot, it might not count, though. Possibly subverted in that he seemed to actually care about him.
averted in that Pintsize doesn't actually realise that the other robot is male until well into the date, and isn't too happy when he DOES realise
Pintsize also remarks that robotic gender is more a matter of opinion than fact, that robot "sex" is basically electronic and it's entirely possible to have 'sex' without actually knowing the gender of the other, and generally making it clear that his male-perv persona is basically an artefact of his programming
Marten and Dora take a long lunch, and return with Marten wearing some of Dora's clothes. Everyone assumes that they had done something naughty, but Marten claimed that they had been ambushed by Shaolin Monks and spilled spaghetti sauce on his clothes and needed to change at Dora's. Everyone laughs it off, but a strip later he is proven correct when a battered monk arrives at the coffee shop and recognizes Marten.
Also occurs in the explanation for Steve's infrequent appearances for a long stretch of the comic. The two possible explanations were "he got drunk and dicked around for a while" or "he became a secret agent and blew up an island," and it was implied that not even he knew for sure which was true. Until later, when he ran across The Baroness from his story.
Clinton: JUST YOUR DAD? He helped develop the first true AI! He invented the quasiperpetual myomer! He's the Henry Ford of intelligent machine design! He pioneered sustainable AI-controlled orbital habitats! He designed the microsatellites that keep earth's albedo stable! HE INVENTED THE ROBOT HAMSTER!
Art Evolution: The art style has and continues to evolve, and comparing the newest strip with the first one shows how striking the development has been.
Jeph has redrawn (in his new style) a number of early strips for his books, as he'd lost the original high-resolution art. The result is... striking.
Ascended Extra: Angus. He appeared multiple times as a joke character, then popped into focus after Faye dropped Sven. Now he appears regularly, and has important relationships with other characters, particularly Faye.
Short-haired girls. Jeph had to promise when Penelope was introduced not to "cut all her hair off" in an art-style change like he did most of the others (Hannelore once lost nearly all of her hair in mid-conversation with Marten & Steve as Jacques changed his mind on how it should look).
You could count "girls with issues" into the Appeal-factor as well, considering how nearly the entire cast features them. The men are generally more weird and dumb/confused than neurotic.
In interviews, Jeph has attributed to the high proportion of female characters in the cast to his finding female forms more interesting to draw, in contrast to male forms which are more flat and, in his opinion, boring.
Dora. She was "outed" as bisexual in the comic (to readers, not to the cast) when she told her then-boyfriend Marten that she realized her sexual attraction to girls after seeing pictures of a female fetish model - Marten's mother. No one bats an eye at her considering a relationship with Tai.
Breakout Character: Hannelore won a character poll by a landslide naming her as the most popular character, shocking the author. Quite a ways for what was a supporting one-note character added to an already sizeable cast.
Broken Aesop: In-universe. After hearing about the childhood accident that gave Clinton his robotic hand and that he actually prefers it, the others reflect the moral this teaches kids is that "messing around with fireworks gives you cool robotic limbs!"
Marten and Dora have at least twice come up with ridiculous stories as to why they were running late, one involving a bunch of Kung-fu monks, another a Deathbot 9000 that Pintsize had insulted on the internet. Marten individually seems to have a knack for winding up in situations like this.
Marigold blurts out what she doing after realizing lying about being in the bathroom instead for that six hours is an Embarrassing Cover Up. Marten and Hannelore don't believe it (would you believe she was eating cookies and watching anime with the head of security instead?), and assume she's having digestive problems.
Catch Phrase: The phrase "Hurr hurr hurr!", meant to sarcastically imitate laughter from stupid or inane people, has been uttered by nearly all of the main cast at some point. Jacques clearly does it himself, judging by newsposts.
Cerebus Syndrome: The strip started as a boy and his robot, but in no time moved to sarcasm and joking about music and music fans, while developing the relationships between the characters before taking a turn for the dramatic about #500, while retaining the joke-a-day format. Jeph lampshades this in the commentary/news for strip #1481.
Faye is the undisputed queen of this trope: When she first appears, her behavior is fairly run of the mill, if somewhat short tempered (her response to being asked if it's ok for Marten to ogle her: "If I sense any ogling, I will stab you and then poop in the wound"). After a while, she becomes perky and cheerful, but violently short tempered, (she once threw Pintsize across the room for a comment about her ass), and also stopped using contractions. Then after a while, she became the cynical snarky person she is now. She's also using contractions again, despite the fact that trait got an explanation in-comic. Comparing Faye today with one of her two earlier incarnations, one could very easily be forgiven for thinking them totally different characters.
Children Are a Waste: This is what many characters seem to agree on implicitly. In several cases justified since they came from families where something went wrong. However, apparently not even Marten Reed seems to think that the world needs another Marten Reed. Jeph has expressed the same opinion in the footnotes that accompanied one comic where this was expressed, so it's apparently an opinion he shares. Later on averted where Faye says she might consider having kids later in her life, indicating her view on the subject may have evolved.
Sara. Created without any real character, she just vanished after Dora appeared. It became a long-running gag that she was "eaten by an Allosaurus", but no characters would ever mention her after the first 100 strips except in one or two Mythology Gags: in 149 Dora mentions leaving Sara in charge of the coffee shop, and her absence is lampshaded. Also counts as a case of What Happened to the Mouse?.
Steve lampshades one of his first disappearances when he returns in the guest comic, coming gasping out of the hall closet. When Marten asks what he is doing there he says:
Steve:What am I doing here?!? I have been locked in the hall closet for months! Didn't you people notice I was missing?!? Why didn't anyone come looking for me?!?
Steve: Lemme get this straight - you EXPLAINED to her that this whole Elliot drama bomb was basically your fault. Marten: Yeah. Steve: And that turned into a depressing conversation about how much she misses her poor, sick grandmother. Marten: Uh huh. Steve: But then that somehow inspired her to ask you to go dancing. Marten: *sigh* Yeah... Steve: And for SOME GODDAMN REASON, you're SAD ABOUT THIS. Marten: I don't know how to dance!
Therapist: Have you tried, ah, self-stimulation? Faye: Oh yeah. I also drink seltzer when I want soda, eat rice crackers when I want chocolate, and listen to bluegrass when I want death metal. I am getting a freaking Popeye forearm. My right hand filed a RESTRAINING ORDER.I AM JUST A TINY BIT BORED WITH IT.
Luna: I saw... I saw a tunnel of light, with my granddad waiting at the end, waving to me... Marten: Jesus, I thought she was going to go all Temple of Doom on you and pull your heart out through your chest!
The Singularity happened (offscreen) in the comic, creating a supersentient AI. The other AIs are pissed that they're not part of it, the humans are a little freaked out but getting over it, and the AI itself just wants to talk to people. It tried talking to dolphins, but apparently they're really creepy once you can understand them.
Don't Explain the Joke: Two for the price of one! Claire makes a Stealth Pun by sticking a "Like" sticker on the novel Faye is reading, and when no-one gets it she proudly explains "I put a like on Faye's book!" Then The Rant further explains "IT'S A FACEBOOK JOKE." (For that matter, the title of the strip is "Say It Out Loud".)
The coffee shop at the center of the series is called Coffee Of Doom. The sign on its bathroom door says "Restroom of Doom!", exclamation theirs, though they once lovingly referred to it as "The Cave Of 40 Asses".
Faye, who acknowledges that she used to be "a bitch with issues" but is now just "a bitch" used and sometimes still uses Marten as a punching bag for no reason. It's sort of lampshaded (the trope in general, not Faye's treatment of him specifically) by Marten. And Faye beats up on everybody, regardless of gender, but when she goes too far she's always put in her place, and she goes to therapy and actively tries to be a less crappy person despite her issues. Marten takes a lot, but he won't let her seriously hurt him, and he often hits back with his own brand of snarking. She is also verbally abusive to the coffee shop customers, but this actually gets good reviews and hipsters coming in for a daily dose of snark.
The VespAvenger hunts abusive boyfriends, but the main cast doesn't think it's acceptable. They lampshade it by suggesting that a guy on a Harley who beats up abusive girlfriends would be unacceptable, but VespAvenger states she would hook up with such a character.
An attendant trope in play is Abuse Double Standard Abuse Human On Robot. Entirely apart from Pintsize getting his head caved in, or being embedded in the wall (which is usually deserved), many of the main characters refuse to respect Momo's boundaries, e.g., Faye lifting Momo's skirt to check out her crotch ("Just curious!"), or Emily repeatedly poking her in the navel after it's revealed that this changes her hair and eye color, despite Momo repeatedly telling her to stop.
Dream Sequence: Here, here, and here. To quote Deathmøle Jacques, "I could do one of these dream-comics for every single character and I STILL wouldn't be tired of the conceit. I am so weird."
Drink Order: As with real-life indie coffeehouses, Coffee of Doom customers are advised not to use Starbucks' faux-Italian size names, at penalty of markup. Over-flavored or overly-pretentious drinks are likewise bad ideas. Though if you're hazing a newbie, anything goes.
Drop-In Character: Hannelore lives in the apartment above Marten and Faye and is a frequent visitor, not just there but eventually to the homes of other characters as well. Inverted here where Hanners comes home and unexpectedly finds visitors.
Drowning My Sorrows: Happens quite often, what with all the issues and drama the characters suffer.
In-universe, Faye calls this on suicide jokes. In response, Angus calls it on jokes about Marigold.
Which she inevitably breaks less than two months' worth of updates later. As the linked comic demonstrates, her casually insulting sarcasm doesn't really have an off switch (aside from having her mouth duct taped shut).
Claire: Fairly well-adjusted, but most likely went through self-identity issues before she realized for good that she is transgender and brought her life in line with that reality.
All of the other characters have more-or-less normal backgrounds, as far we've been told thus far. Yes, this is counting Marten's mother's job, as that doesn't seem to have caused Marten any trauma other than the occasional bit of needing Brain Bleach. It does seem to have given him a rather less-than-normal outlook on certain things, however.