Fanfic is full of examples of historical misunderstanding, particularly when you get into the distant past--that ancient time before say, last week.

Here are some of the most WTF I've seen:

Titanic:

Jack and Rose boarding a jet in 1912 (commercial jet travel didn't come about until the late 1950's; commercial air travel of any kind wasn't around until the 1920's, and then only for the well-to-do).

Mary Sue wearing a miniskirt on the Titanic--and no one blinking an eye.

Mary Sue fucking all the officers--and being cheered on.

Jack hearing Rose's voice in a movie in 1925 (the first talkie was in 1927).

Jack calling 911 in 1917 (911 did not exist until the late 1960's, and then only in limited areas).

Jack and Rose taking a trip to France for fun in 1917 (lots of people were going to France in 1917, but they were there for the war, for the most part; WWI pretty much brought European tourism to a standstill, and nobody in their right mind would take their children on a tour of an active war zone).

Jack and Rose dancing to disco music at their wedding in 1912.

Everyone congratulating Rose on her out-of-wedlock pregnancy.

Jack and Rose living together without benefit of marriage--and no one blinking an eye.

Any songfic using a song written after the year it was set in.

Pirates of the Caribbean:

Jack Sparrow examining a color photo of Mary Sue--in the 1700's. (The first photograph was taken in 1825, the first photograph of a person in 1839, and the first color photography came about in 1908).

Jack Sparrow fighting alongside Benjamin Franklin and George Washington in the American Revolution in France in 1917. :suspect:

Across the Universe/Hairspray/Mad Men/Outsiders/Anything Else Set in the 1960's:

Cell Phones
CDs
E-mail
Internet
My Chemical Romance and other modern bands
Open and universal acceptance of homosexuality
21st Century Movies (not originals of remakes)
"Ive nevar herd of the cold war"
"Ive nevar herd of Vetnam" (I've never heard of Vetnam, either, but Vietnam--half my male teachers growing up were veterans.)

To be fair, there are so many anachronisms in Pirates of the Caribbean that it might as well be an alternate history world.

I'd contribute more, but since my main fandoms tend to be 'modern, only with better technology' I don't really have much to say.

Aubrey/Maturin
-Women being captains in the Royal Navy in the early 19th century.
-characters with names like Samantha and Brianna in the early 19th century.
-The existence of photography.

Les Miserables
-The Amis being contemporaries of the French Revolution

Notre Dame de Paris/Hunchback of Notre Dame
-Asians being in medieval Paris
-Women wearing short skirts without any adverse reaction
-Girls running off to join the Gypsies, without being rejected and ejected.
-Medieval Paris being clean
-The majority of Parisians being literate.
-Women talking back to people in authority without consequence.
-Minorities being regarded as equals.

Whoa, you replied while I was editing.

A LOT of slash runs into this. Do people really not know that in the lifetime of the current U.S. president, it was still possible to be involuntarily committed to an insane asylum on the basis of having voluntarily had homosexual sex with a fellow adult? Or that you could also be charged and convicted as a criminal purely for said acts? Where are the angsty love stories based on experiencing The Love That Dare Not Speak Its Name? No, the only people who are opposed to two men sleeping together are the evil harpies who seek to keep them apart. (Never mind lesbian love. It doesn't exist except in fics labeled PWP. Even though it achieved grudging social acceptance in some parts of the English-speaking world much earlier than being (gasp! shock!) exquisite.)

Marauder-era Harry Potter fanfics are a goldmine for this. In the mid 70s everybody had internet access, mobile phones and liked bopping to Avril Lavigne, apparently.

Urk, that's me being innocent for a change. I was assuming 'teabagging' meant the act of taking the nutsack into one's mouth, not getting someone else to do same. *blushes with innocent maidenly modesty*

I just got a PM from a fanbrat who wants me to post her story on my website. I read it over, and discovered that alcohol is illegal in the United States.

Yes, Prohibition was never repealed in this author's world.