There is nothing in Stone's obituary that Richard Evans is revealing for the first time, as evident from the numerous quotations by others that Evans draws on to provide backing to his characterization. Episodes such as own obituary for E.H. Carr, published in London Review of Books as "Grim Eminence" were infamous at the time, Evans himself calling it in In Defense of Historya "notorious demolition job". In context though, it should be understood that he was 'returning the favor' for Carr's review of The Eastern Front 1914-1917 several years earlier. In truth there are so damn many different things mentioned in the obituary that doing justice to all of the would be futile, so I will focus only on one, namely the poor quality of his scholarship, and leave it to others if they wish to weigh in on other parts of his biography.

There are two points to focus on here, the first is Evan's marginally kind words for his best known work, The Eastern Front 1914-1917, of which he writes:

In 1975 he published the book that made his reputation: The Eastern Front 1914-1917, which won him the Wolfson history prize and numerous laudatory reviews. This was a scintillating narrative based on a wide range of sources in several languages, including both Russian and German, admirably succinct and clearly argued. It did a great deal to redress the imbalance of the British historiography of the war, which had up to this point focused almost exclusively on the western front.

It argued powerfully that administrative chaos and poor military and political leadership were more important in causing the Russian defeat than economic weakness. However, its approach was self-confessedly old-fashioned, with its concentration on grand strategy, political and military leaders, to the neglect of the experience and morale of the ordinary soldier, factors that feature strongly in more recent accounts.

The second is his utter denigration of subsequent works, which take up too mush space in the review to cite completely, so I'll only note what Evans says about the final work of his, Hungary: A Short History, but take it as indicative of the sentiment throughout:

Knowing that he did little research, never bothered to check his facts and relied on his literary flair to mask his mistakes, the publishers got serious historians to go through the text: one of them sent in a 20-page list of errors, but it was impossible to spot them all and so it was left to reviewers to point out the many further inaccuracies.

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Evans is being quite fair to The Eastern Front 1914-1917, a work which still remains one of the few fulls texts on that theater published in English. If anything, he is being more than fair as while "concentration on grand strategy, political and military leaders, to the neglect of the experience and morale of the ordinary soldier" wasn't all that unusual for military history being produced in the 1970s, reviewers were finding other faults as well, such as Peter Kenez who wrote that "in spite of its virtues this is an extremely irritating book" before running through its various faults and concluding that "this book should be read, but with caution". And of course, to return to Carr, his own review was quite unsparring, calling out Stone for taking on too much of a task and refusing to admit it:

The result is a muddle. An overweight of factual and statistical information, often on minor topics, alternates with slapdash impressionism on major issues; and there is little in between.

The book survived those reviews to nevertheless thrive, but at least in part due to the dearth of alternatives, the next publication of a general work in English not coming until 2016, and which one reviewer praised as a "very necessary reexamination of the Eastern Front" in direct reflection on that gap.

Looking at his more recent output though? Well, Evans certainly doesn't hold back, but neither did anyone else. I'd start with Evans' own review of Stone's World War Two: A Short History as the backhanded compliment that Stone isn't even good ad being bad any more is quite biting:

Perhaps the most disappointing aspect of this book is its unremitting dullness. Normally, one expects from a book by Stone outrageous expressions of bias, opinionated obiter dicta, pungently expressed prejudices, quirky judgements and entertaining oneliners. In nearly 300 pages, I could only find one piece of the old Stone, where he refers to the French soldiers defeated by the Germans in 1940 as “the very picture of the demoralisation of Third Republic France: dirty, sullen, cigarette-chewing, and smelling of cheap wine” (in reality, the French fought bravely: more than 90,000 were killed or went missing in action). If there had been more of this kind of thing, the book would have been a good deal more readable.

It isn't like others felt much better though. Richard Overy cut even deeper, perhaps, with the succinctness of his opening line when he wrote:

The one good thing about Norman Stone's sequel to his brief history of the first world war is that it is short.

He then went on to decry:

Anyone who chooses this as their first book on the second world war by 'one of Britain's greatest historians' (Penguin's words, on the cover) will be bombarded with errors and false statements.

Several of examples were provided. And other works were no less spared. His The Atlantic and Its Enemies: A History of the Cold War got it from just about every corner, although Richard Mullen's brevity perhaps captured the overall sentiment best:

Basically the book can be summarised by one sentence in its Introduction: I was right'.

This of course girds the truth of Evans' criticism in the obituary when he notes how Stone's books became more his personal gripes and opinions than history, and other reviewers agreed too to be sure, such as Jonathan M. House who kept it a bit more subtle, but no less biting if you know what "deserves careful reading" means in the code of academic reviews ("this is a minefield of bullshit"):

In short, The Atlantic and Its Enemies is a monumental effort of research and original interpretation that deserves careful reading by historians of the period. It is regrettable that Prof. Stone's opinions are so interwoven with his research that it is sometimes difficult to assess the historical value of the result.

Similarly Mark Byrnes wrote it off for similar self insertions, as "Stone's personal history is too personal to be of much general interest." This doesn't even begin to get into other, more offensive issues, such as Stone's self-imposed exile to Turkey where he became a vocal denial of the Armenian Genocide, but would require quite a large tangent to address in full.

Now, of course, you also asked how, despite all this, he maintained his reputation, which I would again note that Evans merely echoes the facts when he wrote:

Journalists often described him as “one of Britain’s leading historians”, but in truth he was nothing of the kind, as any serious member of the profession will tell you.

Even Evans readily admits that in his heyday Stone was a personality and that made him a darling of popular media even if shunned by many in academia. Taking up journalism, he wrote numerous articles for non-peer reviewed venues like newspapers, and apparently was not known to turn down a chance to appear on TV either. He served Thatcher as an adviser, and even as a speechwriter, which certainly polished his reputation as well, most especially in conservative circles (and ruined it further in others, such as the Oxford student body). Similarly while reviews found in peer reviewed journals might often savage him (and to be sure, not every review was entirely negative), non-academic reviewers, especially ones to whom there was ideological affinity, would continue to provide write-ups like "The Atlantic and Its Enemies a worthy addition to the essential Cold War canon".

This gets us to the final part of your question though, what are we supposed to make of this? I would first note that none of this is new. While Stone himself set the tone in a way with his attack on Carr after his death, as already illustrated, Evans is no stranger to taking Stone to task, nor was anything else in the obituary new revelations to which he never knew and could not defend. He was a controversial figure in life, and if anything, reveled in that. But while they aren't new in of themselves, they were new to many.

Stone was still well known by many unaware of his darker side, or at least its extent, and his reception within academic circles. Someone's death is a time to review their life, but for someone like an historian, whose work lives on after them, it is also a time to review their work. There have been several notable authors who, in the past, upon hearing of their death, I cracked open something they did, either a reread or something new, and I'm sure this is no different, and this is where it is important to mind the context of what Evans did. Compare Evans' obituary which cuts right to the core, to that published by the Centre for Eurasian Studies for which he had served on the board, "Maverick Historian and Turkey's Great Friend Norman Stone Passes Away" which openly lauds him for his genocide denial.