That QI programme is bollox. Its funny an all, but you wouldn't want to trust it as a source. The age of consent in Vatican City is 14, same as Italy.
The claim is sometimes found that "In the Vatican State, there is an equal age of consent set at 12 years of age",[41] but this is not correct. The misunderstanding derives from the fact that Vatican Law follows Italian law. In 1929, when the Lateran Treaty was signed, the age of consent in Italy was 12,[42] and so the same was true then in Vatican City. However, since that time the Italian law has been changed, and so the laws of Vatican City (in accordance with the policy that was in place until January 1, 2009) changed automatically with them. Since there has been no change in the Italian age of consent since January 1, 2009, the two remain identical with no further review by the Vatican.
http://en.wikipedia.org/wiki/Ages_of_consent_in_Europe#Vatican_StateSpain has the lowest age of consent in Europe at 13.