"How then are we to look for love in great cities, where selfishness, dissipation, and insincerity supply the place of tenderness, simplicity and truth?" (1.5.3)
St. Aubert sets himself up as the great judge of human civilization more than a couple times early in the book. It's no surprise that Em thinks she can place quick judgments on people, given her dad's grandiose tendencies.
"Good God!" exclaimed Emily, "what an opinion must he form of me, since you, Madam, could express a suspicion of such ill conduct!" (1.12.36)
You tell her, Em! There's nothing Em hates more than being pre-judged. Kind of ironic, don't you think?
Though she knew, that neither Morano's solicitations, nor Montoni's commands had lawful power to enforce her obedience, she regarded both with superstitious dread […]. (2.3.113)
How's this for messed up? Em regards the word of Montoni as law—she has no other choice. Montoni's judgment is all that matters.
His fears had often since appeared to her prophetic—now they seemed confirmed. (2.5.109)
As we've mentioned, it doesn't take a lot for Em to pass judgment on someone. Valancourt's warnings that Montoni is bad are more than enough for her imagination to kick into overdrive.
[…] Montoni consented to secrete him for a few days till the vigilance of justice should relax, and then to assist him in quitting Venice. (2.6.20)
When Montoni gets mixed up in Orsino's nonsense, he basically brings the book of the law down on himself. As they say, choose your friends wisely…
"And is he come to Udolpho? He does well to endeavour to conceal himself." (2.12.9)
When Em learns that Orsino has arrived at Udolpho, her worst suspicions about Montoni are confirmed. Udolpho is the furthest reaches from the law.
"You have murdered her then! I am talking with a murderer!" (2.12.55)
The scariest thing to Em is associating with a known criminal, and (she thinks) Barnardine fits the bill. Do you think her curiosity is piqued?
"Judging as I do," resumed Montoni, "I cannot believe you will oppose, where you know you cannot conquer […] if you have a just opinion of the subject in question, you shall be allowed a safe conveyance to France." (3.4.12)
Once again, Montoni is setting himself up as the Supreme Justice of Udolpho. It's scary to think that under his brand of law, murderers get away with anything they want.
"It is her very self! Oh! There is all that fascination in her look, which proved my destruction!—Retribution?—It will soon be yours, it is yours already." (4.16.10)
Agnes basically sets up a little trial for herself. Since Em looks exactly like the woman she murdered, it's almost like she's doling out a slice of justice to herself.
"I then was innocent; the evil passions of my nature slept." (4.16.29)
Agnes presents a picture of what she looked like prior to committing the terrible crime. Does she really succeed in purging her conscience through her conversation with Emily? Is justice done?