I love the comment re: Genghis Khan: "Oh, COME now!"

Well, I guess I don't need to fret anymore about the fanfics I'm writing. One's based on a computer game in which the devs had a character quote Richard III when Shakespeare wasn't born for another 500 years! (the game starts in the year 1039 and references events from 1008 - at least, since we don't know exactly when the heir's parents actually married, only that the heir was born in February 1009).
Another several in progress are based on BBC Merlin. There are a lot of anachronistic elements in that show. My story is a crossover with Highlander/Highlander: The Raven (I plan to make one of the characters Immortal and two others already are for reasons in the show itself, so I've got about 1500 years to fill and have been trying to decide when and where they go while not copying any of the historical events from the two Highlander TV shows).
However, while tomatoes and modern prom dresses show up in Merlin, my own story is going to involve some research to make sure it's doable. Someone edited the historical flashbacks from the Highlander series into 4 very long YouTube videos, giving - in chronological order - where Duncan MacLeod was and when in each of the 4 centuries he's lived. It's a treasure trove of information and I see the showrunners took care not to have him travel unreasonable distances too quickly or have him be in two places at exactly the same time (same year, but the travel times are plausible by horse or by boat across the English Channel).
Of course the Xena showrunners couldn't care less about all this.