This question refers to Alma 7:10, where Alma prophesied that Jesus Christ "shall be born of Mary, at [the land of] Jerusalem which is the land of our forefathers." It is noteworthy that Alma did not speak of Christ being born in the city of Jerusalem, but at Jerusalem. This is a significant difference.
There are at least two possible explanations for Alma 7:10 That offered by the critics is that no prophet named Alma wrote these words. They assume that Joseph Smith wrote the Book of Mormon, and at age 24, didn't know that Christ was born in Bethlehem. This idea is illogical considering that nearly everyone at the time of Joseph Smith understood that the Savior was born in Bethlehem. It is also inconsistent because Joseph Smith is recognized by even his most hated enemies as a person of unusual intellect.
The second explanation--accepted by most Latter-day Saints--is that in the year 82 BC, Alma did live and taught that Christ "shall be born of Mary, at [the land of] Jerusalem which is the land of our forefathers" (Alma 7:10). Proof of the historical and linguistic accuracy of Alma's statement is found in the Armana letters, where it is recorded that in Palestine and Syria, a large area around a city and all the inhabitants of that area bore the name of the city.
Bethlehem is only five miles south of the much larger city of Jerusalem. Thus, a citizen of Bethlehem could have accurately described himself as a person who lived "at Jerusalem." Rather than Alma's comment being evidence of Joseph Smith's fraud, it is in reality a confirmation of his inspiration.
Today, the further we are away from our home or any specific town, the more likely we are to "lump it" with the closest large metropolitan area. If we are visiting New York we might tell people we are from Salt Lake City rather than Bluffdale, Utah. If we are in Europe we might tell someone that we are from Utah, or possibly we might say we are from the United States. When we say that, we aren't in error; we are just not being as specific as we could be.
A final thought: if Joseph Smith or later Church leaders felt this to
be an error, why didn't they "correct" it and make it one of the many "wholesale"
changes the detractors are always accusing the Church leaders of making
in the Book of Mormon? Latter-day Saints find no contradiction with Christ
being born "at Jerusalem," the land of the forefathers of Alma and his
2 Kgs. 14:20 "And they brought him on horses: and he was buried at Jerusalem with his fathers in the city of David."
Bethlehem is the city of David. This verse is more specific about the location but it's interesting to note that it starts out with the phrase "at Jerusalem" and then clarifies the location by the denotation of City of David.
Sperry, Problems of the Book of Mormon, pp.131-36.
Nibley, An Approach to the Book of Mormon, pp.80-82.