Removed these items from the trope examples list because they're general observations, not specific examples, but preserving them here in case somebody wants to use them as the basis of an Analysis page:
All Women Are Doms All Men Are Subs: Though without sexual meaning, many, if not the most relationships in his books are female-led and man is submissive. Dmitri Karamazov even says "I believe that every good man must be kept under the heel of some woman!", which may be the view of Dostoyevsky himself (or not).
Author Tract: Liable to appear at any given time in his books. However several critics note that what appears to be Author Tract turns out to be different from Dostoevsky's own ideas.
Christianity is Catholic: Averted. Although he was a devout Christian, Dostoevsky loathed Catholicism (especially the Jesuits), and he saw the raw, innocent spirituality of Russian Orthodoxy as an antidote to it. An Author Filibuster in The Idiot is devoted to this.
There is actually a very good reason for this: Dostoevsky, like most Russian (and European in general) novelists of the time, had his work published in installments by literary magazines which paid by the page or word; the longer the work, the more money you made.
Also for most of Dostoevsky's career he wrote short stories and novellas — Poor Folk, The Gambler, The Double, White Nights, The Eternal Husband, Notes From Underground — he only wrote four major novel-length narratives, but those are among the best ever written.
Epilepsy: Dostoevsky was a famous real-life epileptic who often suffered periodic fits. His family and friends noted that his fits came suddenly without warning and that he would describe his trance-like state and visions in considerable detail. This eventually made its way into his books where many characters, notably Prince Myshkin and Smerdyakov are epileptics and a lot of Mind Screw comes from their descriptions of their fits.
Loners Are Freaks: Dostoevsky's books feature characters who are loners, social rejects, the mentally ill and other freaks. His sympathetic portrayal of their alienation from society struck a chord with several modernist writers and made him highly popular among existential philosophers. What people often miss is that Dostoevsky doesn't romanticize this status at all, as seen in Notes from Underground. His works show how poverty, breakdown of family relations, genuine social dissatisfaction and callous cruelty makes such figures easy to indoctrinate into radical politics or other kinds of dangerous abstract ideas. About the only response to such alienation Dostoevsky can find is either authentic religious belief, The Power of Love, forgiveness and compassion.
The Masochism Tango: The relationship between any given Dostoevsky character and any other given Dostoevsky character.
Misaimed Fandom: A posthumous example. Dostoevsky wrote about revolutionaries or aspiring radicals, social rejects, outsiders and featured characters who tend to scorn family values and religion. This made him influential on leftists, philosophers, freethinkers and young adolescents despite himself being a conservative Orthodox Christian Russian writer. One delicious irony for the Great Russian is the fact that his books influenced Franz Kafka and Sigmund Freud and several other Jewish writers like Isaac Bashevis Singer despite being, unfortunately, an anti-Semite like many Russians of his time.
Sliding Scale of Idealism Versus Cynicism: Dostoevsky's books tend to break the scale, as they have the entire range of behavior — from the most idealistic to the most cynical, with everything in between — existing at the same time, while being inconclusive as to what wins out.
Straw Nihilist: Dostoevsky codified these characters in many of his books. Raskolnikov is perhaps the archetypal example. Other examples include The Underground Man and Arkady in The Adolescent. Bear in mind that this is a case of Unbuilt Trope since Dostoevsky was a rough contemporary of Nietzsche but did not read his books, while the latter read his books after formulating some of his beliefs and noted how Dostoevsky anticipated his ideas.
Removed these items from the trope examples list because they're general observations, not specific examples, but preserving them here in case somebody wants to use them as the basis of an Analysis page: