Under Russell T Davies' revamp of the programme, there has been a deliberate avoidance of stories set on far-off alien worlds. Inevitably, this leads to an increase of stories set in Earth's history. So it's no surprise that they finally got around to the Romans again.
All the stories set in the past since the revamp have been pseudo-historicals, and 'The Fires of Pompeii' is no different. There is an alien invasion, and in order to save the planet, the Doctor has not just to allow Pompeii to be destroyed, but to cause it to happen. In the end, this is actually a cheat as far as answering Donna's question goes. But the show's never really found a better answer to 'why can't the Doctor change history?' over the past forty-five years.
On the subject of cheating, the episode chooses to take a particularly apocalyptic view of Pompeii's destruction. This is probably the way most people think it happened, but the evidence actually suggests that the eruption of Vesuvius took the best part of a day, and, whilst accurate figures are impossible to calculate, a portion of the population will have escaped. It wasn't quite the complete extermination of a whole city that this episode implies. And as for the Romans not having a word for a volcano - well, strictly speaking that's true, but only because what they had was a three-word phrase. They were certainly aware of volcanoes - Etna was active at the time, and there are suggestions in some writers that Vesuvius was suspected to have had a volcanic past.
But this episode isn't a history lesson. Rather, it's a very knowing manipulation of lots of things that people know about the Romans, stuffed full of jokes. It won me over right at the beginning with a comment on how long it's been since the show went into Roman times, and then a direct reference to that particular story. It followed that up with a joke about Mary Beard's dormouse test, and then the best Spartacus joke since Life of Brian. And that's before we point out (as Davies freely confesses in Doctor Who Confidential) that all the character names for Peter Capaldi's family are lifted from the Cambridge Latin Course.
Another point at which I suspect the script is being deliberately knowing is in the opening scene. The Doctor thinks he has arrived in Rome, and only after seeing Vesuvius does he realize he's in Pompeii (why doesn't he consider the possibility that he might be in Herculaneum?). But of course, the sets he has been walking around are Rome, in a way. These are the sets that were originally built for the HBO/BBC series Rome. Credit must go to the production designers and director, who have dressed and shot these sets so that it's isn't immediately obvious that they are the same sets (this becomes plain when you watch Doctor Who Confidential, where the more obvious buildings are not hidden). Production values are high, and it certainly doesn't look like they only actually had 48 hours to film in Cinecitta.
It's interesting to compare this story with the audio adventure 'The Fires of Vulcan', produced in 2000, which was also set in Pompeii at the time of the eruption. It's not unknown for the new series to borrow from audios (Rise of the Cybermen' takes elements from 'Spare Parts', for instance), and the title of the later story is almost certainly an acknowledgment of the earlier one. But beyond that and the setting, the two stories share little. 'The Fires of Vulcan' is an actual historical, and uses historical characters (if sometimes anachronistically). It owes a great deal in terms of structure and scenes to Edward Bulwer-Lytton's 1834 novel The Last Days of Pompeii. In 'The Fires of Vulcan', the Doctor again can do nothing for Pompeii - but he does not try himself to escape, instead believing that he himself is fated to die in the eruption.
Overall, 'The Fires of Pompeii' is an extremely interesting piece of classical reception, and a pretty good episode of Doctor Who to boot. Though I could have done without the stunt casting of Phil Cornwell. And the last shot is utter nonsense.