Clarity is expressing yourself in a way that allows readers to follow what you are saying. It minimizes the risk of misinterpretation. Clarity contrasts with obscurity. Obscurity leaves at least some readers in the dark about your meaning. I like the quotation from Searle. I like another quotation from the author Robert Heinlein too: 'Obscurity is the refuge of incompetence'. Obviously in some sorts of writing obscurity doesn't matter so much: some writers want to be interpreted in a variety of possibly contradictory ways. But Philosophy shouldn't be like this.
(Ht: Duck) I may be idiosyncratic in my views here, but I think this use of 'clarity' is confused and obscure, for a straightforward set of reason. Either we understand clarity to be a feature of the writing, or a feature of how it is read, or a feature of what is expressed in the writing (and thus understood in the reading). It's natural to understand clarity to be a feature of the writing, and this is how Warburton at first glance goes on to characterize it, condemning Heidegger for polysyllabic abstraction. But that's an odd sort of condemnation. For instance, well-written papers in mathematical logic or category theory are said to be clear in this way: everything is laid out straightforwardly, simply, with good organization, careful analysis, precise argumentation. But it would be nonsense to suggest this allows readers in general to follow what they're saying, or that it minimizes the risk of misinterpretation in general; and mathematicians certainly don't avoid polysyllabic abstraction. This is because any difficulty in interpretation would be due to the difficulty of the subject itself. So if we're taking clarity to be a quality of the writing, it's simply false to distinguish it from obscurity by saying the latter leaves "at least some readers" in the dark about your meaning; readers in general will have less difficulty understanding an obscure news report than understanding a lucidly clear paper on string theory.
One possible way to get around this would be to restrict the domain of readers that count. But if we do this, we are giving up the notion that clarity is a quality of writing; rather, it is a proportioning of the text to the response of readers. Then clarity really becomes (by definition, I would imagine) that which risks less misinterpretation. But here we run into the question of which readers are supposed to be the standard. Clarity understood this way reduces misinterpretation, but by whom? The simplest way to characterize the domain of relevant readers is to treat it probabilistically: the relevant readers are those who were most likely to read it in the first place, or were the most likely to read it with interest in the first place. But this means that Heidegger can't be judged by any standards but how well people who are likely to read Heidegger with interest tend to understand him. This can be determined only by looking at how well they actually do understand him; you couldn't possibly do it by pointing at Heidegger's text, because if you aren't in the domain of relevant readers, your opinion about his clarity doesn't count, and if you are, you might well be the outlier in the group.
Warburton clearly wavers among all these. Consider the sort of obscurity he associates with his six levels of clarity:
(1) polysyllabic abstraction, "i.e., hiding behind long words" (note the choice of the term 'hiding' here)
(2) passive constructions or convoluted syntax
(3) poor use of paragraphs, which "often indicates poor argument structure" (again, note that the writing is supposed to indicate -- on what evidence I don't know -- something about what is expressed)
(4) "Philosophy involves building a case for a conclusion. The reader needs to be able to see how evidence, argument support the conclusion which purportedly follows from them." (Here we find an appeal to what the reader is able to see. I should point out, incidentally, that Descartes's first Meditation, which Warburton notes as an exemplar here, is very regularly misinterpreted on this very point. Readers usually miss the fractionating nature of the argument. That is, Descartes doesn't argue in a straight line. Instead, he presents a reason for doubt, then a reason to doubt the doubt, then a reason to think that we can have some certainty despite this doubt, then another (stronger) reason for doubt, and so forth. The pendulum swings back and forth, but at every swing more is loss to doubt, until we reach the possibility that God, or some proxy, might be a deceiver, in which case all our reasoning becomes suspect. I cannot count the number of intelligent readers of Descartes's Meditation who haven't caught on to the way Descartes is building a case, but instead see the Meditation as a series of more or less isolated arguments rather than a back-and-forth, despite the fact that that's obviously what it is.)
(5) Lack of illustrative examples: "When philosophers omit examples or applications of their ideas they sometimes float off into realms of imprecision - not all their readers will be happy to float off with them." Again, the reason given for considering this a flaw in writing is that it is a (possible) sign of imprecision of thought.
(6) This is poor underlying thought, and so it's obvious on what line it follows.
If we make clarity a matter of writing, we can save some of these levels. Clarity becomes a matter of word choice, sentence structure, and paragraphing. But then paradigm instances of clear writing, which use polysyllabic abstractions, passive constructions, and even convoluted sentences in order to be precise and in order not to be misleading, fall on the obscure side. (We also end up condemning people on grounds that seem inadequate. Is "The stone is lit by the sun" more obscure than "The sun lights the stone"?) Warburton thinks Hume clear. His contemporaries were split on the subject, many thinking him obscure, continually making strange word choices, structuring his sentences in curious ways, and perpetually stating things ambiguously. Samuel Johnson refused to consider him seriously as a writer of English at all; and it is certainly one of the reasons for the popularity of Beattie's attack on Hume that Beattie was almost universally recognized as the clearer writer, with a better grasp of the English of England, with which Scots of the time (including Hume) continually struggled. (We tend to forget that the English of Scotland was much less closely related to the English of England in the eighteenth century than it is now. The two have grown together, in part because of the hard work of the Scots of Hume's generation to show that they could meet the English intellectually on their own ground.) And it must be confessed that the history of Hume scholarship shows that Hume's contemporaries were at least right about his tendency to convolute his claims to the point of ambiguity. Hume, who has shown himself one of the easiest authors in the common curriculum to misinterpret, shows precisely how vague and shadowy the notion of clarity here must be.
If we make clarity a matter of underlying thought, then all these verbal issues become simply secondary, and the primary question is not whether Heidegger uses big words or complicated sentences but whether he reasons well with them. Hume is clear not if he avoids misinterpretation, but if he knows what he's talking about. And so forth. But then all the talk about passive constructions seems useless.
I think despite its use as a shibboleth, very few people have any clear idea of what they mean by "saying something clearly," and only an obscure notion of what they mean by "obscurity". Warburton's mysterious quality, which now supervenes on sentence structure, now on the underlying thought (where 'clarity' suggests 'having a nose for the subject', however we are supposed to determine that on the evidence of the text itself), now on how the writing tends to strike readers (although we don't know which readers), jumping from one to the other without any rhyme or reason, is, I think, typical.
The real value of clarity, to the extent that it seems worth paying attention to at all, has nothing to do with sentence structure as such; you can't inculcate it by telling people not to use passive constructions. The real value of clarity is not a well-defined trait at all. There are no sharp lines between obscure and clear; you cannot say, "Heidegger is obscure, Searle is clear" as if people fell into one category or the other. I would suggest that clarity is connected to what the eighteenth century Scots would have called good taste. Unlike most contemporary philosophers who chatter about clarity, the Scots actually went to great lengths to clarify what good taste was. There are some variations from account to account, but, roughly, to have good taste with regard to some activity or product (like painting or paintings) is to have a broad sympathy with people who are well acquainted with a broad range of examples of that activity or product so as to have developed the skills required to make refined discriminations and accurate comparisons with regard to that activity or product. Thus, having good taste in paintings means having a sense of how people who know paintings well would tend to judge paintings (generally by being such a person oneself). The only thing that seems to be in the vicinity of what contemporary philosophers mean by "saying something clearly" is "saying something in a way that would be approved by someone with good taste in reasoning". The rest is fluff, as far as I can see.
But it must be admitted that I have a taste for eighteenth-century theories of taste, and tend to see them as one more way in which eighteenth-century Scots philosophers were cleverer than their rather unimpressive modern-day Anglo-American cousins.