For the ancient world, a famous factual error is the story that Rome, after destroying Carthage in the Third Punic War, sowed its fields with salt so nothing could grow there again. It's a great story, and you'll find it in hundreds of modern books about the Punic Wars, but it was invented in the 19th century.

In fact, the Romans rebuilt Carthage, and turned the land around it into one of the most productive agricultural regions of the empire.

This is why it's important to fact check secondary sources against the primary sources they cite to see if the claims are actually supported by the evidence.

See Ridley, R.T. (1986). "To Be Taken with a Pinch of Salt: The Destruction of Carthage". Classical Philology 81 (2): 140–146.

There is a notorious incident when historian Thomas Lowry forged a document signed by Lincoln. On April 14, 1864, Lincoln pardoned a Union soldier for desertion. However, when Lowry got his hands on it, he changed it to 1865, making it look like Lincoln issued the pardon shortly before his assassination. He wanted Lincoln's last presidential act to be something significant so that he could claim credit for discovering it.

The forgery was seen as a legit presidential act for over ten years until he finally fessed up to crime after people started being suspicious of the document's accuracy.

You can read an article about it here:

http://www.outsidethebeltway.com/abraham-lincoln-last-official-document-forged/

In my own research, I have also come across some factual errors in books, but nothing of any real significance.

Everybody knows that Washington Irving made up the story about George Washington and the Cherry Tree. Fever people know that he also wrote a mostly false biography of Christopher Columbus. The most compelling story from it was the idea that before Christopher Columbus, everyone thought that the earth was flat. In fact we'd known that the earth was round since the Ancient Greeks did the math to figure it out. More problematically, Irving also semi-founded the myth of Columbus as a great man.

Edit: I can't spell George.