Quote 1
"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.
Quote 2
"Let's not be hasty." Jace was actually grinning, the bastard. […] "[Simon's] cute like that. Look at his little pink nose." (13.115)
Even the third-person narrator thinks Jace is being a "bastard" for teasing Simon. And when the narrator thinks you're a jerk, well then you know you're on thin ice.
Quote 3
"[Simon] just looks dim-witted. Really his intelligence is quite average." (13.215)
Jace is so jealous of Simon, he can't resist making sarcastic digs at him even when Simon's no longer human. But seriously, what's Jace's beef with the guy, besides the fact that he's Clary's bestie? This makes it clear that, as awesome as he may seem, Jace is not the most mature of folks.
Quote 4
"Declarations of love amuse me, especially when unrequited." (3.57)
Jace's amusement at unrequited love is ironic because he has his own unrequited love for Clary, his sister. He'll get down off his cynical high horse soon enough.
Quote 5
"Falcons are not meant to be loving pets: They are fierce and wild, savage and cruel. This bird was not tamed; it was broken." (11.160)
This story told by Jace says a lot about why he puts up a prickly façade to keep people away. He's both scared of loving and being loved. Vampires on the other hand? Not scary at all.
Quote 6
"My oath to the Covenant binds me," [Jace] said. "No such oath binds you." (8.60)
Here, Jace is telling Clary that she can tell Simon all about the Clave, etc., because she isn't forbidden to do so. We have a feeling that Jace wouldn't tell Simon anything even if he had a gun pointed at his head. There are some rules you just don't break.
Quote 7
"Only people with no purpose are unhappy. I've got a purpose." (10.260)
We wonder if Jace is trying to convince himself that he's happy here. After all, his purpose is little more than a supernatural assassin, which sounds like it might be more than stressful and less than fulfilling.
Quote 8
"I may not believe in sin," [Jace] said, "but I do feel guilt. We Shadowhunters live by a code, and that code isn't flexible: Honor, fault, penance, those are real to us, and they have nothing to do with religion and everything to do with who we are. This is who I am, Clary." (19.122)
Jace's job defines him. Talk about a workaholic.