Well, yes. Hadrian's Pantheon was built around AD 125, and was a radically new design at the time. The dome was the most original feature, but not the only one (and interestingly the original production sketches for the show also included a dome). Rome is set in the 50s and 40s BC, and it's most unlikely that there was anything that looked like the Pantheon around at this time.
However, there's more to this story than simply dressing up a set with an anachronistic building because it's Roman anyway, and most of the audience won't notice. The background for the Radio Times cover is a composite made up of elements of the Cinecitta set, rearranged for impact. But all the buildings are to be found on that set. Looking at the HBO site, it is apparent that this particular building is meant to be the Senate House, sitting in the north-west corner of the Forum Romanum. Now, it happens that there was indeed a circular edifice at approximately this point in the Republican period. It was not the Senate House, but the Comitium, where sat the popular assemblies of the Roman people, the ones which, in theory, elected the magistrates who ruled Rome. And it wasn't a building, but a circular square. The actual Senate house, the Curia Hostilia, was a rectangular building adjoining the Comitium to the rear. But this is a distinction one can expect a work of fiction to pass over. I don't believe that the real Republican Curia was anything like as elaborate as the building that Rome's producers have put in its place - with the portico, which the Curia certainly lacked, this is more elaborate than the Curia Julia built by Caesar after the Republican Senate house had burnt down - but more thought has gone into this bit of the set than might first appear.
There seems rather less justification for the Temple of Venus which the set designers have placed next to the Senate house, but perhaps they should be allowed some artistic license. But how much artistic license should be permitted to a series that, like many epics in the past, trumpets its 'authenticity'?
Is it enough to permit the triumphal arch in the corner of the Forum? This arch is modelled on the Arch of Titus, dedicated in AD 81. But there were certainly triumphal arches in the Roman Republican period. And there was indeed a triumphal arch where this one has been placed. But that was a triple arch, rather than the single one built for the set. And it was erected in 19 BC, commemoration of Augustus' diplomatic triumph in Parthia (which was regularly portrayed in imperial iconography as if it was a military victory).
Which leads on to one last thought. The first season of Rome goes as far as the assassination of Julius Caesar. It has been renewed for a second, which presumably will cover the war with Caesar's assassins and the Second Triumvirate, and take the story down to the battle of Actium in 31 BC and the defeat and deaths of Antony and Cleopatra. (According to this piece, James Purefoy, who plays Antony, has been contracted for six years, but even if one assumes it takes two years to make a season and that the six years includes the two spent on season one, it's hard to see how he can get that much work before his character is eliminated.) If it goes to a third season, that would presumably (as Penny Goodman has opined) deal with the reign of Augustus. This was a period of unprecedented development in the Forum - so will the Cinecitta set be torn down?