(1) He says:
But what really convinces you that what you do as a Christian of any denomination is the right thing to do is what theologians in the eighteenth century, the great period after the Newtonian revolution of the seventeenth, called "Christian Evidences."
What puzzles me about this is that this is, as far as I can see, anachronistic. 'Christian Evidences' is a nineteenth-century term. I can't think of any work prior to the 1800's that uses the term [i.e., in this precise sense], and (while its datasets are somewhat patchy) Google N-Gram bears out my memory (looking at the datasets, at least some of the pre-1800 bumps are clear false positives, e.g., a magazine issue filed under the wrong date). To be sure, there were things done in the eighteenth century that would later be called Christian Evidences (especially on the subject of miracles), usually arising from anti-deist arguments, but it's really the 19th century that consolidates Christian Evidences as a field and gives it a name. And it's not surprising why -- there is one author who, above all others, contributes to making it a distinctive and unified field, and that is none other than William Paley, whose View of the Evidences of Christianity, published in 1794, is what really gave the term its vogue as Paley became more and more a key part of standard curriculum in the nineteenth century. All those manuals of Christian Evidences are imitating, refining, correcting, and building on Paley. It's a nineteenth century thing.
(2) Hoffman says that Hume appeals to "common sense"; but a reading of the essay shows that this is not at all that to which Hume appeals. He appeals rather to some controversial elements of Humean epistemology. For instance, he appeals to the counterpoise of ideas, an idea that was roundly ridiculed for nearly a hundred years as incoherent and absurd, because it makes sense only if you have essentially conceded all the major points of Hume's particular variety of empiricism.
(3) Hoffman identifies as Hume's conclusion what is in fact only the conclusion to Part I. Now this gets into thorny interpretive territory -- there is no general agreement among Hume scholars as to what, precisely, Hume means by the conclusion of Part I. But one thing that is quite clear is that, however it is interpreted, it is not Hume's conclusion, but a secondary conclusion on the way to his conclusion, which is that, while there is nothing that absolutely rules out reasonably believing a miracle has happened on testimony, if the testimony is sufficiently good (he explicitly gives a hypothetical example later in which he proposes the testimony would be sufficiently good), nonetheless religious miracles and especially miracles serving to found religions, always involve so much potential distortion of judgment by the passions that no testimony for them has ever reached the level of testimonial quality that would be required.
However, much of the post is quite interesting, and the history of how the essay was read is definitely worth some reflection.
Nearly everyone thought that Hume's essay on miracles was obvious sophistry when it came out; and within a decade and a half of its publication, it was generally thought to have been decisively refuted by George Campbell's Dissertation on Miracles. Within a century, it was widely thought to have been devastatingly ridiculed by Richard Whately's Historic Doubts Relative to Napoleon Buonaparte. Babbage's Ninth Bridgewater Treatise, published in 1837 and despite the name not actually a Bridgewater Treatise, put Hume to the test of Bayesian mathematics and concluded that the theory of probability told against Hume, and proposed a computer-based model for miracles that got around all of Hume's strictures. Ironically, Christian Evidences probably helped keep Hume's argument alive: it was the best argument against believing in miracles available, so it became the argument everyone refuted. But the refutations passed, as fashions pass, and Hume had even then, here and there, his defenders. And after the fall of British idealism, the rise of respect for Hume in general began, and Hume's discussion of miracles benefitted from more sympathetic readers who had never even heard of Campbell, knew nothing of Whately's mockery, and had never read Babbage's non-Bridgewater reflections on the Bridgewater approach to natural theology.
And thus the essay on miracles sees the rise in its fortunes as it increasingly became a staple of undergraduate philosophy courses, a rise that went largely unabated until Earman's publication of Hume's Abject Failure (in, if I recall correctly, 2000) revised and extended Babbage's argument and led to the current state of the field, which consists largely of anti-Hume Bayesian interpreters (building on Earman), pro-Hume Bayesian interpreters (increasingly, it seems, a minority, although it has some notable defenders, like Peter Millican, although most of them will now also argue that the pure Humean argument needs modification), and a very diverse group of people like myself who, despite having no problem with Bayesian statistics, think Bayesian epistemology is cracked, and don't think Hume's epistemology is accurately represented or reasonably interpreted in Bayesian terms at all. The only real agreement on Hume's essay these days is that it's hard to interpret. What's the actual relation between Part I and Part II? What does Hume mean when he talks about weighing entire proofs against each other? What is the underlying theory of laws of nature in the argument? What's the actual relation to Tillotson's anti-transubstantiation argument, which Hume claims (almost certainly with deliberate mischief) is parallel? Does Hume's argument, especially in Part II, really have the adequate explanation for the propagation of miracle stories that it would need? What is the point of the eight days of darkness example? Does the argument he gives actually yield the conclusions he says it does? Why does he end up restricting his claim to religious miracles? All of these are currently matters of some dispute. After being read for decades as pretty obvious and simple, it is now read as a thornily difficult bit of argument, even by people who think the argument works. Part of this has to do with the turning of Fortune's wheel with regard to the interpretation of Hume himself: in the nineteenth century he was largely read as a pretty wacky and immoderate skeptic, full of paradoxes that were built on arguments that, while perhaps clever, could never convinced a reasonable person because they would require him to affirm ignorance about things like whether he was the same person yesterday that he is today. For much of the middle of the twentieth century he was read as a positivist avant la lettre. As positivism itself declined, he began to be read as a mildly skeptical naturalist, cresting perhaps with the New Hume debate, which is still in some sense going on. And it's still too early to say how this century will treat Hume. Every phase of interpretation has reinterpreted the essay on Miracles to read Hume in its own light, so it has shown itself to be amenable to a rather wide variety of interpretations.