Does modern art matter? In 1980, in The Shock of the New – a BBC television series-turned-book – Robert Hughes convinced millions of sceptics that it did. Shock was a powerful antidote to the Kenneth Clark style of TV art history. Hughes was a straight-talking Australian; there was no posh, languid reverence in his presentation. His message was that you didn't have to like 20th-century art (in fact he happily pointed the finger at some that was pretentious, overvalued and bad); but you did need to see how art contributed to the great debates of the period, from technology to the politics of social change.

It must have been a hard act to follow. Since 1980 Hughes has continued to work as a critic; he has written, among other things, a bestselling account of British transportation of convicts to Australia (The Fatal Shore) and a volume of memoirs; and he has weathered accusations of plagiarism, a near-fatal car-crash and years of litigation that followed. Now in his 70s, he has brought out Rome, a cultural history of the city he first visited in 1959; it is a narrative that stretches from Romulus and Remus to Berlusconi.

Reader, be warned. Skip the first 200 pages and start this book at chapter six, "The Renaissance". By the time Hughes reaches this point, he is well in command of his material and is on characteristically cracking form. He offers some delicious pen portraits of the artists and architects who designed and made what are now the tourist high-spots of the city: the Sistine chapel, the Piazza Navona, St Peter's basilica, the Campidoglio. Particularly vivid is his discussion of Bernini, "the marble megaphone of papal orthodoxy" – who was loathed by most visitors in the 19th century ("intolerable abortions" was Charles Dickens's description of Bernini's monuments), but increasingly admired in the 20th. And he nicely captures the spirit of the 18th-century grand tour. The desire of the young milords to discover the grandeur of ancient culture was only one side of the story. Sex tourism was the other. Rome was, as Hughes observes, the Thailand of the period, and he includes plenty of revealing stories about the brash bigwigs who turned up in the city: Lord Baltimore, with his harem of eight women, or Colonel William Gordon, who (if Batoni's famous portrait is anything to go by) pranced around the Mediterranean in a kilt and swaths of his family tartan. What on earth did the locals make of these people?

In his epilogue, Hughes, the modern cultural critic, elegantly savages the mass tourism and commercial culture of Berlusconi's Italy. A visit to the overcrowded Sistine chapel has become, he insists, close to unbearable, "a kind of living death for high culture" – which can only get worse "when post-communist prosperity has taken hold in China", and the Chinese flood in by the million. The same, he might have added, is also true of St Peter's basilica itself. It may be large enough inside to hold huge numbers of visitors in relative comfort, but they now have to go through a metal detector to get into the place. When I tried to visit one afternoon last December only two of these machines were working, and people in the queue winding around the piazza would have been waiting for more than an hour.

So what is the answer if you really do want to see the Sistine chapel in some peace and quiet? It is "to pay what is in effect a hefty ransom to the Vatican". For you can now book a two-hour visit to the museum plus chapel in a small group after closing time (with a guide "whose silence", as Hughes ruefully notes, "is not guaranteed"). This gives you a full 30 minutes to view the Michelangelo ceiling, in the company of no more than 20 other people. The only trouble is that it costs €300 a head, and the enterprise is run by outside contractors who are presumably splitting the profits with the church. This is, of course, typical of 21st-century Italy's approach to its heritage (the new director of the Ministry of Culture is apparently "a former chief of McDonald's" and the restoration of the Colosseum is to be sponsored by an upmarket footwear company). "If you don't like it," Hughes shrugs, "you can always write to the Pope; or else buy some postcards and study those in the calm and quiet of your hotel."

So far, so good. In fact, the second half of the book is an engaging history of this wondrous city, very much in the tradition of The Shock of the New, packed full of sharp observation and trenchant one-liners, artfully and fearlessly told. The first half of the book, especially the three chapters dealing with the early history of Rome, from Romulus to the end of pagan antiquity, is little short of a disgrace – to both author and publisher. It is riddled with errors and misunderstandings that will mislead the innocent and infuriate the specialist.

True, the occasional mistake in detail can sometimes be a price worth paying for the kind of long view that Hughes attempts to take here, covering almost 3,000 years of history. If a book is brave enough to think big, we can perhaps forgive a few errors with the proper names (of which there are several in Rome – "Miltiades" the famous fifth-century Athenian general, for example, being curiously substituted on one occasion for "Mithridates", the first-century king of Pontus). But Hughes has made more than a few pardonable slips. The "ancient" parts of this book are littered with howlers. Sometimes, for example, CE and BCE are confused (so that Julius Caesar's Gallic enemy Vercingetorix is said to have been beheaded in 46CE, almost a hundred years after Caesar himself was assassinated), or the correct chronology is flagrantly reversed ("a succession of autocrats, starting with Augustus himself and continuing onwards through Pompey and Julius Caesar", he writes, when in fact Pompey and Caesar preceded the emperor Augustus). On other occasions, the identity of the characters is hopelessly muddled. Hughes clearly has not been able to distinguish "Pompey the Great" from his (very different) father, also inconveniently called "Pompey".

Beyond such basic errors, there are also plenty of wider historical misunderstandings. Hughes somehow manages to attribute the foundation of the Colosseum to the wicked emperor Nero, when in fact the whole point about the Colosseum is that it was founded by Nero's successors as a propaganda coup against him. (Vespasian and Titus built it, with the spoils of the Jewish war, as a place of popular entertainment, open to all, on the very spot in the centre of Rome where Nero had established his exclusive and very private pleasure gardens.)

His characterisation of Roman pagan religion as full of "nature spirits" until the poet Ovid invented deities with personalities in the first century BC is a caricature even of the views of the antiquated text books he cites in his bibliography; and no decent scholar of Roman religion has suggested anything like that for half a century. In one of the most gratuitous howlers, he claims that the great altar of Pergamon (in modern Turkey), now on display in Berlin, was "torn asunder and looted by German archaeologists in the 19th and early 20th centuries and shipped, section by damaged section, to Berlin" – as if we should be imagining its desecration by a bunch of Teutonic Lord Elgins. In fact, the altar had been ruined for centuries when the German archaeologists arrived; they set about finding and gathering together its widely scattered fragments.

The list could go on.

We often talk about the decline of interest in the classical world. But, so far as I can see, interest in antiquity is as strong as ever (and, to give him his due, Hughes has seen that it is impossible to talk about modern Rome without acknowledging its dialogue with the ancient city). What has declined is any sense of obligation to write about the classical world with care and knowledge. Any old stuff will do and almost no one notices.

If a book about the history of the 20th century had as many mistakes as this one, I am tempted to think that it would have been pulped and corrected. It certainly would not have been widely praised and enthusiastically recommended as Rome has been.

Mary Beard's Pompeii: The Life of a Roman Town is published by Profile.