Loch Ness Monster
This example was recommended by Mark Harris.
On 21 April 1934, the Daily Mail published a photograph of the Loch Ness monster which is commonly known as the "surgeon's photograph." The photograph is now accepted to be a hoax.
It is important to note when discussing misleading and fake news that discrediting a particular piece of evidence does not discredit all evidence. For example, the fact that the surgeon's photograph is a hoax does not mean that the Loch Ness monster does not exist.
Suggestions for Further Reading
"Loch Ness Monster Sighted." History Channel.
Lyons, Stephen. "The Legend of Loch Ness." Nova. 12 Jan. 1999.