We were watching Season 2, Episode 10 of the 2015 television series Poldark, which is set in the fourth quarter of 1793. Dr. Dwight Enys, heartsick for a woman who has rejected him, has decided to enlist in the Royal Navy as a surgeon and fight against Revolutionary France. Here he is at the recruiting station.
The only problem is that the White Ensign and the Union Jack on display here are anachronistic: they are the versions employed after 1801, following Irish parliamentary union (itself partly a response to the revolutionary wars). (This is to say nothing about whether floor stand flags would be on display like this in Britain in the late eighteenth century.)
And this is a British show! I would expect this sort of mistake with Murdoch Mysteries, but not from the BBC.
Here is the same error made closer to home – specifically, on a poster up at Reinhardt last year. Even the Betsy Ross flag dates from 1777 at the earliest.
UPDATE: In Season 3, Episode 3 of Poldark, we see that the producers haven’t procured the correct version of the Royal Arms either. This appears on the wall behind George Warleggan as he acts as the local Justice of the Peace.
Yes, the image is rather blurry, but it clearly shows 1. England, 2. Scotland, and 3. Ireland, with the fourth quarter somewhat obscure. The arms of George III in 1794, however, looked like this.

Wikipedia.
That is, in the first quarter we have England impaling Scotland (for the parliamentary union of 1707), while in the second we have France, illustrating the king’s ancient claim to be the rightful ruler of that kingdom, which he only relinquished in 1801. The fourth quarter shows the Hanoverian territories on the continent. It would appear that the royal arms shown in Poldark are those of Queen Victoria.
Once again, I acknowledge my pedantry and wet-blanketness. But I still say that with a little extra effort, you can minimize such mistakes, and thus not alienate those audience members who might notice them. There are plenty of underemployed historians out there who would be happy to help out! I would add that while absolute accuracy might not matter all that much with eighteenth-century heraldry, it might be more important when depicting other times and places. Imagine a movie that showed, say, a Sioux encampment of teepees, each one with its own totem pole and/or inuksuk in front of it, to give an authentic “native” cast to the scene. Anyone with half a brain would be able to see that this represents an amalgamation of three quite distinct Native American cultures, and would be a major insult to the people in question. So if you get into the habit of thinking accurately anyway, it will help you avoid charges of insensitivity when the topic is politically significant.