As recently as last year, claims were made that Leonardo forged the Turin Shroud using pioneering photographic techniques and a sculpture of his own head. Leonardo’s forgery was apparently commissioned to replace an earlier 14th century version of the shroud that was exposed as a poor fake. The theory says that this earlier shroud disappeared at around the time of Leonardo’s birth and when it reappeared some fifty years later, it was hailed as a genuine relic, because it was really his convincing replica. If anyone could have done it at that time, Leonardo would be a likely candidate, but it’s a fairly implausible theory.
The article also addresses the conspiracy theory that Leonardo da Vinci painted Mary Magdalene into The Last Supper. I recommend the article. It is short and to the point.