In a time where people rarely traveled more than 20 miles from their village, world-wide has a different connotation.
As far as the size of the ark, it is quite possible that the critics are wrong. It is also possible that the animals involved were LOCAL animals, leaving out elephants and penguins.
The primary purpose of the story is obedience to God and the cleansing of the area to remove iniquity. The BBC is simply doing their best to denigrate the Bible, as apparently that is part of their charter.