Henry VIII and Katharine of Aragon sitting down to a nice pot of tea.
And my favorite, which is not so much an anachronism as the author's own weird pet theory: that the companion of a princess was called a "countess" because it was her job to count how many times the princess was alone with any particular man; if the tally reached a certain number, the princess then had to marry the man in question! What, diplomatic marriages? Betrothals (and sometimes even weddings) between two children still in the cradle? Piffle, I say! Nope, if she's alone for 5 times with my low-born rascal of a hero, she has to marry him. That's my story and I'm sticking to it!
ETA: sometimes even non-fiction reference books get things wrong. I'm thinking about a book on medieval cookery that said there are no extant period recipes for bread, and that no one knows what skirrets are/were. Mistress Jaelle of Armida, an SCA cooking Laurel, dispelled both of those, and showed me the definitive proof. (Skirrets are a root vegetable, BTW.) Sometimes "no one knows" means "I, the author, don't know, and I can't be bothered to dig through obscure reference books to find out."