South America has been suggested as a possible site for Book of Mormon lands. This theory requires some major geographic changes to make it possible. The most common proposal suggests that the Amazon basin was at a lower elevation and was underwater before the time of Christ. This created a narrow neck somewhere in eastern Peru or Ecuador, the land southward being south of this narrow neck, and the land northward to the north. At the time of Christ's crucifixion the surface of the land was changed (elevated in this case) resulting in what we see today.
This proposal is favored by the presence of the advanced Inca civilization which inhabited the area. However there are a number of major obstacles to the theory.
First, if we can move oceans and continents to suit our theory, there are no limits to what could be proposed.
Second, most of the geographic references were made by Mormon 350 years after the changes which took place at the time of Christ. There was still a narrow neck during his time and some of the last battles were fought there.
Third, there is no geologic evidence that the Amazon basin was underwater during Book of Mormon times, or for that matter, any time during recent geologic history.
Fourth, the Andean chain of mountains are too massive and elevated to allow for a narrow neck, even if we were to lower the continent by a thousand feet.
Fifth, it doesn't match the criteria for Book of Mormon lands listed in the text.
Sixth, Joseph Smith's opinion in the Times and Seasons (Vol. 3, #22) indicating that the land of Zarahemla was in Central America would tend to eliminate this location.