Shelley isn't big on the subtle showing. She pretty much tells you what characters are like through bits like this:
The gentle words of Agatha and the animated smiles of the charming Arabian were not for me. The mild exhortations of the old man and the lively conversation of the loved Felix were not for me. Miserable, unhappy wretch! (13.19)
Only, hold on. Since all of our narrators are first person, everything we know about everyone comes through a biased narrator. There's actually no real direct characterization at all: it's hardly any different from hearsay and gossip.
Okay, pretty obvious: Shelley is clearly saying something about the relationship of looks to character. But she kind of distances herself from saying that ugly people are evil by having the characters themselves use looks as a tool of prejudice and unwarranted characterization. Since the monster is ugly, he must be evil—Agatha is so upset by his appearance that she actually faints. The fun part comes in when the monster actually does become sort of evil, or at least commits evil crimes. He conforms to everyone's expectations. He becomes the victim of his own characterization.
Oooh, this should be fun.
The kicker? The monster. Without a name, he's completely cut off from society. He literally has nothing tying him to anyone else in the world. You can't even talk to him, because there's nothing to call him.