A. W. Moore discusses Leibniz's optimism (i.e., the idea that this is the best of all possible worlds) in The New Statesman. It's interesting, and nicely laid out, but I think it fails as a discussion of Leibniz (although not necessarily in other ways, e.g., as a discussion of a particular view of the world). When Leibniz talks about the 'best possible world', he means the world-history that simultaneously optimizes simplicity of means and richness of effects -- simplicity and richness being criteria for assessing decisions and plans precisely as decisions and plans. Moore technically recognizes this but makes the mistake of assuming that Leibniz thinks of this as a matter of trade-offs between simplicity and richness rather than as a standard that requires trade-offs among other goods; and his argument does not actually do any justice to Leibniz's idea here.
It's worth taking a moment to consider that this is why Voltaire's Panglossian reply does not actually work against Leibniz, because Pangloss regularly ignores both simplicity of means and richness of effect and talks about utility to human beings, which Leibniz regards as a good but not the highest good, or even a particularly relevant good for most things. Moore makes the same error:
Here it’s important to appreciate that even the most trivial improvement in things would be enough to make the world better overall – provided all else were equal. All it would take is a slightly more intense sensation of pleasure whenever you bite into a peach – or, for that matter, when you bite into a peach just once.
But from a Leibnizian perspective, why would a "slightly more intense sensation of pleasure" mean that the world-history in which it happens is better? That is, a world-history is an order, so its goodness needs to be assessed by order-relevant criteria (like richness and simplicity), but why would you think the proper standard of assessment for the entire order of the world is whether it optimizes the pleasantness of a bite of peach?
It's sometimes put forward as an argument against consequentialism that it's extremely easy to formulate crazy consequentialisms, like an ethics in which you should maximize paperclips. The point in the case of consequentialism is usually that you can't guarantee you've found a non-crazy consequentialism unless you know whether actually maximizing whatever it is that your consequentialism requires you to maximize would actually give us a good world. An analogous concern is relevant here. For his argument to work, Moore has to assume at least one of two things. The first is that the pleasure of peaches should be maximized in any and all situations, which is a crazy consequentialism, raising various specters of horrors as now candidates for your best possible world, like a world in which a bite of peach is like heroin and in which the human race eventually goes extinct because the peaches are so good everything else is subordinated to eating them. The second possibility is that there is no quality of a world as world, so that saying that a world is 'better' is just saying that one part of it is better than it might be. This already assumes that it is pointless to frame the matter in terms of 'possible worlds' rather than just particular possible events, since there is no longer any assessment at the level of a world. Everything needs to be assessed on a case-by-case basis, and the criteria for assessment would have to change on a case-by-case basis, since obviously the way in which a bit of peach is better is not the same as the way a student essay is better, and so on for all distinct cases. What is more, it's not clear what the point of this is, because it seems that our assessment would become completely incoherent if we did this, since things can then be 'better' in mutually exclusive ways according to mutually exclusive standards. Maximizing the taste of a peach is better if you are only interested in the pleasure of a peach; it is not better if you are instead interested in accentuating the taste of cream. A taste of potato salad would be a better taste if you really livened up the flavor, it would not be better if you are using potato salad to provide rest from the lively flavor of barbecue -- the blandness is precisely what makes potato salad one of the best barbecue sides.
A more subtle example of the same error is found later in Moore's argument:
Any satisfactory answer to this question had better not ride roughshod over our instinctive abhorrence of the Lisbon earthquake or any of the other horrors and afflictions that blight the lives of human beings. If it does – for instance, if the answer sets greater store by mathematical elegance in the laws of nature than by the relief of human suffering – then it really just changes the subject.
But it doesn't. The direct and obvious point is that there is no reason why one would think that the entire world-history must be devoted completely and definitively to relieving human suffering; Moore needs to establish that our instinctive abhorrence indicates a standard relevant to the whole world and not just to being human. One indirect way to see why it doesn't is to look at the fact that when philosophers try to build an argument from evil, they often have to qualify it by saying that they are talking about 'gratuitous evil'. That is, what actually does the work in most philosophical arguments from evil is irrationality, not evil as such. Our gut reaction is against the evil, whether it's suffering or some other kind. But you can't build a rational argument about how the whole world should be on the basis of your gut reactions to particular parts of it. If you're mad at God for the Lisbon earthquake, even if that's a natural response for a being like yourself, the bare fact that you are naturally angry does not mean that the entire order of the world should have been different.
Moore, I think, is making a mistake that is often made, namely, assuming that a theodicial argument only succeeds if it makes terribly bad things turn out not to be terribly bad things. But one of the reasons why Leibniz is going this elaborate way around in talking about possible worlds is that this is one of the things he wishes to avoid. He doesn't want to deny that there are bad things in the world; he wants to deny that the world itself is bad. He doesn't want to deny that there are things in the world that no wise person would choose for their own sake; he wants to deny that the world itself is one that no wise person would choose for its own sake. He wants to say something like: Yes, you are absolutely right that this or that evil is a terrible thing; you are mistaken in thinking that this recognition is a direct insight into whether this world in which it occurs was worth choosing. You need an argument to move from one to the other. This is why Moore's appeal to Brothers Karamazov doesn't work; it's not an argument, and is indeed just a flat statement that you won't accept any argument at all, that you will in fact insist that there is a problem regardless of anything else that might be said.
(It's also, as a side issue, often forgotten that one of the major themes of The Brothers Karamazov is that Ivan's view is not, in Moore's words, a trump card. Ivan's view is set over against Alexei's view, and Alexei, not Ivan, is the hero of the novel. To put very crudely, Ivan's anger is that God is not a devoted socialist. That's one attitude you could definitely have to evil; but one point of the novel is precisely that there are multiple attitudes you could have, Ivan's is not Dmitri's is not Alexei's, and that the world looks different from each one.)