Clary said, "I'm not blind, you know." "Oh, but you are," said Jace. (1.80)
Jace has knowledge and vision that Clary doesn't, so he can serve as her guide into the Underworld, à la Virgil in Dante's Inferno. Basically, the hottie's here to show her a whole new world.
"Have you had dealings with demons, little girl? Walked with warlocks, talked with the Night Children?" (1.106)
Um, no we haven't thank you very much. Talking cryptically must be in Jace's job description, as Clary's guide to all things magical. It adds to the mystery, sure, but it probably doesn't help Clary much when it comes to sussing out what's real and what's not.
It was as if they had sprung into existence between one blink of her eyes and the next. (1.58)
Clary was either too preoccupied with her fears of a cute boy being murdered that she didn't notice them, or they were somehow hiding in plain sight. But how can people be invisible?
He was tall, with maple-syrup-colored skin, gold-green eyes like a cat's, and tangled black hair. He grinned at her blindingly, showing sharp white teeth. (2.109)
Well this guy certainly doesn't sound like a typical human. He's got a mysterious allure. Must be from out of town.
"Clary, you're an artist. [...] You see the world in ways that other people don't." (2.46)
Art is all about perspective, and Clary's is definitely unique. Clearly Clary's already open-minded enough to see other worlds, other realities, that her fellow mundies might not be hip to.
Clary saw the [police woman's] hand was fleshless, a skeleton hand sharpened to bone points at the fingertips. (4.53)
We would not want to get pulled over by this officer.
"Down the rabbit hole." (6.20)
Jace's allusion to Alice in Wonderland proves that Shadowhunters do read books by mundie authors (assuming that Lewis Carroll was actually a mundie), and that he's about to lead Clary into a world that is both similar to her own and radically different.
"Most myths are true, at least in part." (7.29)
Many characters in the book say this line, or a version of it, making Clary's world, with all its vampires, werewolves, faeries, fallen angels, and more, all the more real.
"Dimensions aren't all straight lines, you know. [...] There are dips and folds and nooks and crannies all tucked away." (7.108)
Nooks and crannies, eh? Who knows what magical worlds might exist inside a Thomas' English muffin? So long as they're butter-filled, we're not picky.
"We all see what we want to see," [Simon] said quietly. (18.197)
This explains the power of magical glamor. When you look at a crumbling mental hospital, that's what you expect to see, and do. But there could be something else there.