These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Beleaguered Assistant: It could be argued that Alec and Isabelle are this for Jace. While he is a very talented Demon Slayer, he is also extremely reckless and very frequently ends up as a Distressed Dude. Early on it is noted that Alec has never killed a demon, despite being the oldest of their Power Trio, mostly because his attention is focused on keeping Jace (and to a lesser extent Isabelle) from serious harm. This trope spreads, almost like a disease, when Clary enters the picture, giving her her own set (mostly Simon and Luke, although Isabelle and the others also take turns). Magnus eventually starts feeling like this for the entire group, since his magic is needed by just about everyone.
Canon Sue: Clary has often been accused of being this. The similarity of her name to the author's doesn't help.
Damsel Scrappy: Clary mostly. Indeed, Simon would be leading a happily mundane life were it not for his determination to protect her even though she just sees him as a friend. Jace could be argued as being a male version of this trope as well, since a great deal of effort on the part of Clary, Alec, Isabelle, Magnus, the Lightwoods, and others centers on saving him from some life-threatening situation that could have been avoided were it not for his nasty independent streak.
Designated Hero - The Clave is an entire group of designated heroes. With their Fantastic Racism, inventive cruelty, and massive arrogance, it's a wonder how we're supposed to root for them in the final battle.
Die for Our Ship - Poor Aline. She consensually kisses Jace once, while he and Clary are still convinced they're siblings, and promptly decides that he's not her type, is a fairly kind person overall (albeit one with no brain-to-mouth filter), and it's implied that she's trying to figure out if she's a lesbian, or possibly even asexual - yet she is constantly turned into a cruel, backstabbing, relationship-smashing harpy who gets between Clary and Jace, especially in AU fanfics.
The release of City of Lost Souls helped the problem a little - it was confirmed that Aline was lesbian, and none of the characters felt any hatred to her.
Kaelie gets this treatment too even though she only appeared twice and doesn't show any interest in Jace at all. Usually in AU's she gets the same treatment as Aline, in series we know that Faeries don't care much for humans.
Ensemble Darkhorse - Clare often expresses her surprise at the fact that many people state Alec as their favorite character as opposed to Jace or Clary.
Harmful to Minors: Although Shadowhunters, like most of modern society, do not consider children to be adults until they are eighteen (which is the youngest age at which they can even attend Clave meetings), it is apparently acceptable for children much younger than that to participate in Demon Slaying. At the start of City of Bones, Alec is the oldest of the protagonists being only one that is eighteen years old. The movie seems to try to avert this by making all the characters a few years older than they are in the books.
Yeah especially if these two quotes have anything to say about it:
Jace: "Do you remember back at the hotel when you promised that if we lived, you'd get dressed up in a nurse's outfit and give me a sponge bath."
Clary: "It was Simon who promised you the sponge bath."
Simon: "As soon as I'm back on my feet, handsome."
Jace: "I knew we should have left you a rat."
"Well, I'm not kissing the mundane," said Jace. "I'd rather stay down here and rot."
"Forever?" said Simon. "Forever's an awfully long time."
Jace raised his eyebrows. "I knew it," he said. "You want to kiss me, don't you?"
Near the climax of the second book, Jace allows vampire-ified Simon to drink his blood in order to heal. This results in Simon with his arms flung around Jace, clutching him violently, and biting his neck. Furthermore, Jace explicitly relaxes and pulls him closer. Uh...
Jace and Jordan have a fair amount as well. . .
Informed Attribute: The parabatai bond. Although it supposedly makes two Nephilim "closer than brothers", Alec and Jace usually seem to have little or no ability to read each other. Alec often fails to get when Jace is being sarcastic (despite the fact that Jace is almost always sarcastic). Jace had no idea that Alec was just pretending to side with the Inquisitor in order to keep her from suspecting that he intended to help Jace. Despite the alleged combat advantages of the bond, they do not really seem any more effective when fighting together than they do with others, such as Isabelle.
This is a pretty sensitive issue to a lot of people, so we won't go into too much detail. But there's a not-insignificant number of people who accuse Clare of plagiarizing several other works, most notably Harry Potter and Star Wars.
There's actually some logical basis in this - Clare copied large amounts of texts from other sources without citing them in The Draco Trilogy: a Harry Potter fan fiction she wrote before City of Bones was published. In fact, the fics were taken down and the trilogy is largely a reworked and renamed version of the fic, plagiarized sections and all. Her fans argue that Clare learned her lesson from that, and that the elements Clare is accused of copying weren't invented by the people she 'copied' them from.
The afformentioned "mundie" term. Also, the only biracial (half-black) character in the series, Maia, is characterized solely by how much violent abuse she's taken in the past at the hands of the men in her life.
Maia isn't the only biracial character in the series. Aline is half-Chinese half-white.
So your (Maia's) boyfriend attacked you, punched you out and bit you, infecting you with lycanthropy, then comes back later, claiming to have only done it because it was the first night of his transformation. You drop him like an old pair of panties, right? No, you take him back, because he obviously didn't mean it! Face. Palm.
YMMV on that one; it could be seen as Jordan having gotten help (which he did) and Maia forgiving him for a stupid mistake that he really is unlikely to do again. Still not great, exactly, but far better.
At one point Clary notices there are no unattractive vampires, and concludes that "maybe ugly people don't want to live forever."
To be fair, it was later retconned - it turned out that the process of becoming a vampire erases visual flaws.
Though that comes with its own set of problems with the othering of people who are at all visually imperfect.
Isabelle takes a fair amount of slut-shaming, while Jace makes out with random people and nobody says a word.
Though to be fair, that's more of a DoubleStandard on the part of fans than a fault of the actual books. In-universe, Isabelle seems to only get flack from her parents (and maybe some of the older Clave members) for dating Downworlders, and that's only ever eluded to and not explicitly shown.
Not to mention most (if not all) of Jace's "making out" are just jokes.