Quote 1
"Oh yes, historians have traced them back to the Middle Ages. They were…A sort of research cluster, to put it in modern layperson's terms. They specialized in a certain type of fallen-angel folklore." (14.47)
If this isn't the biggest clue of all, it's second only to Daniel actually hearing Luce say he's a fallen angel. Miss Sophia's setting down some huge hints here—not only about Daniel's secrets, but also about the fact that she knows what they are and might very well be involved herself. Never invite Miss Sophia to any type of game involving secrecy and deception; she'll be universally bad at it.
Quote 2
"Everyone believes in something. Sure you were baptized?"
"Not if you don't count the swimming pool built under the church pews over there," Luce said timidly, jerking her thumb toward Sword & Cross' gym. (17.143-144)
This little piece of information sets the stage for the giant battle that is about to happen, and it tips the scales of Luce's reincarnation wheel. Without being baptized, as Miss Sophia later explains, Luce's soul can't come back, ever. This matter is no small potatoes.
Quote 3
"I told them you were innocent," Miss Sophia said, turning to remind the officers. "Eerie similarities be damned." (11.120)
In an act of (fake) kindness, Miss Sophia stands up for Luce's innocence even in the face of the condemning evidence. If she weren't such a terrible person, this might make us like Miss Sophia a little bit more.