The story of Pope Joan is an interesting one.

[A] learned woman in male disguise managed to get herself elected pope. She reigned for two years. During a procession on its way to the Lateran Joan gave birth to a child, which in the most dramatic fashion imaginable unmasked the deception. She died immediately afterward. (A History of the Popes, John W. O’Malley, S.J., pg 131-2)

The event was immortalized in several paintings.

But it never happened.

Basically, the stories were believed—even in Catholic circles—for years.

Versions differed of course in detail, including the years when Joan reigned, though it was never set in the present or near-present. What the legend indicated was how ready the faithful were to believe the worst. (O’Malley, 132)

There were a number of versions of the story, which originated in the 11th century and continued through the 17th. Some claim she died of natural causes. Other versions depict an angry mob that killed her after her deception was revealed. Few are specific with dates or years—her reign is usually described as just long ago to not be common knowledge. The biggest evidence against her existence is that there are no substantial gaps in the succession of popes to match the stories.

St. James is the Patron Saint of Spain, and traditionally is held to have been the one to introduce Christianity to Spain, some time before his death in 44 CE (although the truth of this is slim at best).

However, he is best remembered for his supposed appearance in the 9th century, showing up in physical form and leading the Spanish armies to victory over the Muslim force at the Battle of Clavijo, and gaining the name of "Moorslayer". Now, you're probably thinking that didn't happen, and, well, yeah. He didn't appear. But we don't need to base that simply on the fact that it defies reality. Rather, Clavijo, a rather heavy part of the Spanish national mythos, never happened at all. It is a battle which we have no records of for hundreds of years after it was purported to have occurred! So in reality, the two factors which tie Saint James Matamoros to Spain, and make him the patron saint of the country, are probably total hogwash.

Maybe this violates the letter of the trivia question, but the first thing that came to mind are bogus quotations by historical figures. Now a lot of these fake quotes are deliberately constructed for political purposes, find their way into Glenn Beck's monologues, and are quickly discounted by historians. However, there are a number of false quotations that have found their way into the history books. My favorite are those that begin, "While probably apocryphal, Famous Person X is said to have remarked..." In other words, the textbook author knows there's no solid evidence for the quotation, but it serves to illustrate a point, so it gets included anyhow. An old one is Marie Antoinette, "Let them eat cake;" you don't see this one around much anymore, though. One that I've seen repeatedly is Andrew Jackson's supposed response to the Supreme Court case Worcester v. Georgia: "John Marshall has made his decision; now let him enforce it." I'm sure there must be others.

That gunpowder weapons were banned in Japan during their period of Sakoku ('seclusion', 1633-1853) in favor of the sword and connected Samurai tradition. As described in Noel Perrin’s book Giving Up The Gun (1979).

Apparently this period was simply one of relative peace, which meant war was scarce and samurai culture could develop. But fire arms where used throughout the period, here is a nice podcast on the subject.