There are at least three known "Truths" which have appeared on The Unbelievable Truth which are in fact false. One is that you if remove the fleas from a hedgehog, then the hedgehog dies. Another is the cricket did not exist during Shakespeare's time. Both of these were corrected when David Mitchell appeared on an episode of QI in Series F.
The third fact was the origin of the term "Monkey wrench", which occured in the same episode of The Unbelievable Truth in which they corrected a QI fact themselves. This was correct when Mitchell went on an episode of QI in Series K.
Source: QI, Series F, Episode 11 - Film & Series K, Episode 1 - Knees And Knockers
The first person to get all five truths past the rest of the panel was Jo Brand, when talking about Queen Elizabeth I in the third episode of Series 1. Despite this, she also accidentally said something else which was true, and because of the large number of wrong interruptions she ended up in third place with a total of just one point.
The second person to get all five truths past was Alan Davies during the New Year's Special. However, he still finished second. He did it again in the first episode of series seven, which he won.
The third person to do so was Phill Jupitus, in the second episode of the eighth series.
The fourth person to achieve this was Rhod Gilbert in the second episode of series ten. Although he won the episode, his total score in the end was zero.
The fifth person to manage to smuggle all their truths was Lucy Porter in the fourth episode of series twelve.
The sixth person to do the clean sweep was Richard Osman in the second episode of series twenty.
Henning Wehn almost always make a "fake fact" reference to Jesus, or sometimes God ("Jesus's dad") during his lectures. Past "facts" have include Jesus inventing shoes and his name being an anagram of "dog".
Only once has his Jesus fact been a truth - this being that if you believe Mel Gibson, furniture as we know it today was invented by Jesus.
Another time Henning claimed that trees were invented by Jesus's dad. Victoria Coren Mitchell was given 0.5 point on the grounds that God might exist but it is not known for certain.
When talking about the British, Henning claimed that they were not invented by Jesus, but he did invent the song "Jerusalem".
He has also said the vegetarianism was invented by Satan.
Source: Episode 7.5, Episode 12.3, Episode 12.6 and Episode 20.4.
The Unbelievable Truth is currently being adapted for Australian TV by sketch troupe The Chaser.