When the King shows Robert Merivel his building plans to improve London soon after the plague has started, one of the models clearly shows Sir Christopher Wren's St. Paul's Cathedral, designed and built after the great fire of 1666.
A player at three-card monte speaks of being "even Steven". The earliest known records of both the game and the phrase are in the 19th century. Also the queen of hearts he uses is by design and quality from 18th century earliest.
At a very early point in the film, the King says something along the lines of "....and these are your playmates." In the background is a horde of 17th-century ladies boating on the Achille Duchenne water parterre at Blenheim Palace. The palace was not built until the late 18th century, and the parterre was not designed until 1925.
As Robert Merivel and Will Gates are talking in the garden, sitting together on a bench, someone (shadowy) is moving from right to left behind the bushes behind Merivel's back.
When Merivel leaves the Fire of London, he is floating down the River Thames. He is, apparently, discovered 15 miles from Bidnold, which is in Suffolk (unreachable from the Thames)