First, the good news: Everitt's book is clearly written and well organized. He has read a fair amount of the relevant literature, and in his suggested readings at the end of each chapter he is quite evenhanded, recommending books by authors like Richard Swinburne and Stephen T. Davis, with whom he disagrees deeply, as well as books by his fellow unbelievers.
Now the not so good news: Everitt's treatment of the arguments for the existence of God is not particularly sophisticated, and in places he fails to engage with some of the most important recent work. This comes out very clearly in chapter 6, where he discusses arguments to and from miracles. He mentions neither David Johnson's work Hume, Holism, and Miracles (Cornell Studies in the Philosophy of Religion) nor Robert Fogelin's A Defense of Hume on Miracles (Princeton Monographs in Philosophy). He mentions but fails to engage with John Earman's book Hume's Abject Failure: The Argument Against Miracles, a significant omission since Earman's work is inter alia a sustained and sophisticated critique of the conclusion Everitt takes Hume to have established -- that even in the most favorable circumstances possible, it would not be rational to believe that a miracle has occurred. (Everitt, p. 116) The chapter on miracles has no discussion of Bayes's Theorem and the role it plays in contemporary reconstructions of the argument from testimony to the miraculous, though Everitt has (very gingerly) introduced a bit of Bayesian reasoning on p. 77 in his discussion of Swinburne's cosmological argument.
The presentation of Hume's argument against miracles follows J. L. Mackie's presentation in The Miracle of Theism: Arguments For and Against the Existence of God, stressing the claim that if the overall evidence makes it rational for us to believe that a putative event M was a violation of the laws of nature, then that same overall evidence makes it irrational for us to believe that M actually occurred. (See p. 117.) Everitt shows no awareness of the problems lurking here. It is not clear how the inverse claim should be construed (is it the claim that P(M violates the laws of nature) = 1 - P(M actually occurred)? or that for all E, if P(M violates the laws of nature|E) > P(M violates the laws of nature), then P(M actually occurred|E) < P(M actually occurred)? or ... ?); and under almost any interesting construal it stands in need of argument that it never receives. Everitt asserts without argument that if a miracle is a violation of a law of nature it is maximally improbable (p. 115), showing no awareness of the long history of criticism of this claim from the early 1700s onward.
Everitt's attempt to give a fourfold classification of concepts of miracle is another place where deeper engagement with recent work, e.g. Robert Larmer's Water into Wine?: An Investigation of the Concept of Miracle, would have helped him to focus the discussion. Some accounts deserve to be taken more seriously (and understood more fairly) than they are. Ironically, one of these is an account proposed by J. L. Mackie, which Everitt (p. 119) misunderstands and therefore dismisses out of hand. Other, less plausible proposals get nearly equal time. These latter are not exactly straw men, for Everitt does try to find people who have defended them. But those familiar with the field are likely to think that they deserve more neglect than Everitt has given them.
The chapter on the ontological argument is another place where Everitt's presentation is light on detail. There is no discussion of Kurt Godel's ontological argument, for example; and even the versions discussed are mostly informal, verbal versions, though for the discussion of Hartshorne's version he cannot avoid a few lines of modal logic. Here I am more sympathetic to Everitt, since I think that the ontological argument fails in all of its forms. But even the criticisms he levels against Plantinga's formulation, for example, do not do full justice to the subtlety of the argument.
The chapters that attempt to show the incoherence of the traditional concept of God are, on the whole, quite weak. Everitt argues, for example, that Big Bang cosmology shows that past time was finite, and he concludes from this that God, conceived of as an eternal being, cannot exist, since (according to Big Bang cosmology) nothing has had infinite duration. Neither the premise nor the inference is backed by a compelling line of argument. Everitt is following the lead of others and should not shoulder full blame for this particular weak argument. Still, it is a bruised reed for atheism to lean on.
Perhaps the worst chapter in the entire volume is chapter 11, on Arguments from Scale. Everitt urges that the sheer age and size of the universe as revealed by modern astronomy provide evidence against theism. The argument depends entirely on the premise that "humans are the jewel of creation" -- by which Everitt means at least that if God exists, we would expect every aspect of the created universe to be "on a human scale" both temporally and spatially. (p. 215) This claim, however, reveals nothing except the poverty of Everitt's theological knowledge. The whole argument was effectively buried by Thomas Chalmers in his Discourses on the Christian revelation viewed in connection with the modern astronomy (1817). It is painful to see a contemporary author trying to resurrect it in the service of infidelity.
The concluding chapter attempts to draw together the various lines of argument, and naturally the strength of such a summary depends in part on the success of the arguments preceding it. But in this case there are other reasons to be dissatisfied with Everitt's own attempt to sum up his case. He makes some needless and baffling claims, e.g., that one can have empirical disconfirmation for a self-contradictory proposition like (p & ~p). (See p. 304.) Worse, he fails to see how different theistic proofs with somewhat different conclusions may be coordinated in an overall cumulative case for the existence of God, an epistemological issue discussed with great subtlety and finesse by Richard Swinburne in The Existence of God. Of course, Everitt thinks that the arguments are all failures, or at least that they are all very weak. But his substantive evaluation, even if it were backed up by better argument, should be distinguished from the structural question of how a cumulative case is constructed -- not only in religion but in almost any field. Everitt's treatment of this important topic is disappointingly weak.
In fairness, it is very difficult to write a book of moderate size on this vast topic. Mackie's book, for all its flaws, remains the classic treatment of its size. For anything even approaching a full-scale treatment of these issues from the side of unbelief, one needs a work three times as long like Jordan Howard Sobel's Logic and Theism: Arguments For and Against Beliefs in God. But Sobel's book is really written for the professional philosopher who is familiar with modal logic, probability theory, and transfinite mathematics. Everitt's book is not, and for that very reason it is both vastly more accessible and vastly less powerful than Sobel's. Each work has the defects of its qualities.