Of more concern is the way soundbites tend to give an over-simplified impression. Johnson rightly points out that the Roman empire did not have to worry about democracy, but that does not mean, as he goes on to suggest, that the emperor didn't need to worry about the common people of Gaul or elsewhere. No government, be it democracy or military dictatorship, can rule without the overall consent of those ruled. That consent may be obtained by various methods, of which fear is one. But any ruler who thinks that he can ignore public opinion entirely will face the fate of Charles I or Louis XVI.
The canard that the Romans were devoid of racism reappears. You only have to read Juvenal's Third Satire, and the vile racial slurs against the Greeks therein, to realize this is utter nonsense. What was different in the Roman empire was that the dynamic of race operated differently, and it was not such a bar to progress through society as it has been in most European empires. (As Niall Ferguson has shown, some people within the British empire tried to emulate this, and educated Indians, Jamaicans, etc., but were thwarted by the attitudes of ex-pats in the colonies, who imposed a glass ceiling. The result was the worst possible situation, a highly educated native elite with no outlet within the imperial structures for their ambition.) However, as Johnson knows, one had to be careful how much one allowed one's origins to show. One progressed within the empire by being Roman, and too much African-ness or Greekness could be an impediment. Even the African emperor, Septimius Severus, was said to have sent his sister away from Rome because her inability to speak Latin was an embarrassment. (I don't actually believe this story - a daughter of a family with senatorial connections, and therefore potentially a senator's wife, would surely have a decent education in the Latin language - but the important fact is that the story was told.)
Sometimes, Johnson tries to pull a fast one in front of his audience. Much play is made by him that the empire was run by a mere 150 officials in the imperial household. But, as Sander Evans tries to point out to Johnson, this is only a portion of the administrative structure of the empire - to this one needs to add the local elites in the provinces whom the emperor got to do much of the tax-collecting, etc., for him. Undoubtedly the bureaucracy of the Roman empire was smaller than that of modern states, if for no other reason than that it had far less to do, but Johnson has exaggerated to emphasize his point. Similarly he overlooks the subtle but important distinction between worship of a living emperor, which emperors tended to disdain, and sacrifices to the emperor's genius or numen (spirit).
But to a degree these are quibbles. Johnson's basic argument is that the EU attempts to unite Europe as Rome once did, but is failing. Johnson is not, at heart, a Eurosceptic, despite attempts by both pro- and anti-Europeans to paint him as such. He clearly embraces the ideals of European unity and peace, but is sceptical about whether this can actually be achieved. What he believes is that, in order to understand why the EU is failing, one must understand why Rome succeeded. At the end of his investigation, his conclusion is that Rome is not necessarily the best model for European integration. He also rightly draws attention to the problems of getting nations to buy into a pan-European ideal when they still venerate such nationalist heroes as Arminius, Vercingetorix or Boudicca.
I pretty much agree with this. It is all too easy for modern westerners to be naive about the Roman empire, to cherry-pick the good bits and to overlook the less pleasant aspects, such as the fact that it was a military dictatorship. It is to Johnson's credit that he resists such an approach, and suggests that the Roman empire came as a package, and worked because of the unsavoury aspects as well as the attractive ones.
There are a couple of points that Johnson misses that would strengthen his case. Where the EU attempts to create a 'European' culture that stands apart from any one national unit, Rome exported the culture of one single part of Europe to the rest of the continent. More recent attempts to place on single culture in a hegemonic position in Europe have been vigorously resisted by other nations. (Many still resist the EU on the assumption that it is a cloak for French, or German, control of Europe.) It is also worth noting that Roman citizenship gained much of its appeal from its exclusivity. It was achievable, but, until the emperor Caracalla enfranchised every free adult male in AD 212 (as a tax raising action as much as anything), it was not held by everyone, and so it had prestige. EU citizenship, granted to anyone born in Europe, lacks that.
The plea for Turkish admittance into Europe with which Johnson ends his programme is strictly speaking off topic, and of course is something in which Johnson has a special interest (regrettably I only saw a bit of his programme on the recent Turks exhibition at the Royal Academy). But it's also the best bit of the programme. Though Johnson is more dismissive than I would be of continuity of romanitas in the west after Romulus Augustulus' deposition, he is entirely right to draw attention to the fact that the Roman empire continued in the east for another thousand years, and this section allows Charlotte Roueche to make sound points about the western attempt to dismiss the claims of the eastern empire through the invention of terms like 'Byzantine' - western Europe wanted exclusive claim to the inheritance of Rome. As Johnson highlights, the Ottoman empire also claimed the inheritance of Rome, as almost every European nation has. That in itself is not an argument for admitting Turkey into the EU, but Johnson makes a passionate (and right) case that excluding Turkey is based on racism and ignorance, and a retrograde step for Europe. (One wonders whether Johnson intended any irony by recording his vox pop segments showing prejudices about Turkey being illiberal and barbaric in Germany.)
Overall, I would give this programme a B. Pretty good, but not fantastic. But when many television history programmes struggle to achieve a D, that's not too bad, and I certainly wouldn't object to Johnson doing more programmes like this. Let's hope his political career continues to give him time to do so.