Jerkass Woobie: Nastasya Filippovna, full stop. To some extent Ippolit as well.
Memetic Mutation: In some circles, sarcastically addressing someone as "Prince Myshkin" (thereby implying that the person is an idiot) has become a Stealth Insult. This largely grew out of a rather clever joke in The Producers in which Max says to Leo "Yes, Prince Myshkin! What can we do for you?"
Moe: Prince Myshkin has a lot of these traits, being a virginal ill guy who gives off an air of child-like innocence and trust. Needless to say, this being Dostoevsky, things do not go well. Could possibly count as a deconstruction for this reason.