Does Doestoesvki's quote "If God doesn't exist everything is permitted?" contains any logical fallacies?

Is seems to me that the quote has a few underlying assumptions. First, I think that is refers to the God of the Christian Bible. Second, this God is morally good. Third, I appears that one implication of these assumptions is that the Christian God has the absolute standard of morality or something of this kind and therefore his/hers non-existence from which we derive morality would constitute license for every wrongdoing (i.e.,"everything is permitted") . In my view, the fallacy begging the question is present since the "permission" do act immorally already assumes the existence of God that is good and therefore doesn't allow "everything"(sic!). Correct me if I'm wrong, but I also notice some sort of non-sequitur since the conclusion doesn't necessary follow from the premise. I hope I'll receive some illuminating reply(s). Thank you!

I think you accurately pointed out the possible fallacies with this quote. I am not sure how much more I can add. I am just not sure if this has a conclusion or a premise since it is just a question, not phrased as an argument. One of the best ways to get others to see the fallaciousness of "arguments" such as these, is to turn it around using the same form: "If your God wasn't watching, would you rape and murder others?"

The "begging the question" fallacy is not directed at God, it is directed at the belief in the existence of morality.

The original statement can be reworded to clarify this: "If there is no such thing as morality, then every naturally possible act has equal moral value."

The word "God" in the original statement is short hand for "moral law creator/giver".

If one posits a moral law giver that is not God (as a Christian conceives of him), then one has to argue about whose moral law is correct. Since nature itself permits these acts, one cannot use nature as an authority. There is no need to argue about the morality of violating the second law of thermodynamics, for example. This suggests that morality is "supernatural", in the meaning of the word "above the natural."

To address Bo's question: ""If your God wasn't watching, would you rape and murder others?"

One does not obey God's moral laws because of fear (God is watching!), one obeys God because he is the Truth, and the Truth has absolute, unquestionable and universal authority.

If God did not exist, then why wouldn't you rape and murder others? You need merely legally define such acts as not rape, not murder first. We do that today (See: Abortion.)

One of the most successful empires in human history regularly allowed or even celebrated acts that we would today define as rape and murder (See: Roman Empire).

I would also add, that simplified and assuming permitted isn't merely something written down on a piece of paper that people use to justify punishment, The person is merely stating it isn't punishable unless you get caught.....