One thing the Framers had in mind with the Native Born and 14 year requirement was the unhappy history of Poland, where the king was elected for life by the nobility. During the 18th century, foreigners Augustus II and III of Saxony won the throne through a combination of bribery and military pressure. Augustus III's principal rival for the throne, Stanislas Lesczinski (sp?), was the son in law of Louis XV and had lived much of his adult life in France as an exile from Augustus II. The birth and residency restrictions were intended to keep the UK, France or any other foreign power from importing a puppet president.
The requirement that the Electoral College meet separately in each state on the same day instead of at one location was also based on European experience. The election of the Polish king, the Holy Roman Emperor or the Pople was often a buzzard's banquet of foreign diplomats distributing bribes, threats and promises to the electors. Dispersal at 13 or more locations was supposed to make this more difficult, although the problem would arise whenever the election was thrown into the House.