Criticism: There is no evidence for the sudden appearance of written language or change of language in Mesoamerica that coincides with the Book of Mormon.
Response: One of the biggest puzzles about the Olmecs that remains unsolved to this very day is where they came from and how they developed written language and art so immediately. The Book of Mormon offers at least a partial explanation for this question in the story of the Jaredites. The estimated timeline of the arrival and decline of the Jaredites and the carbon-dated development of the Olmec civilization are an uncanny match.
Further, there are numerous articles that address the "disappearance" of the Olmec and the Maya by contending that Mayans are really a later instance of Olmec culture, just as the people of the Yucatan, Guatemala, and Honduras are considered the "lost Mayans" today. They never really went anywhere. Their culture just shifted to a new paradigm and continued. See Takalik Abaj for a textbook example of this (I've visited the outskirts of this site. It's amazing!).
See Ancient City Found in Mexico; Shows Olmec Influence for more about the huge amount we have yet to discover in Mesoamerica (and that is being lost to development every waking moment) and about the Olmec influences on the later Mayan cultures.