Do wrong numbers destroy the truthfulness of The Book of Mormon?
The answer is a resounding no. I explained a few reasons why in this post about millions. But there are more. For example, Chinese writers would want to highlight how the previous dynasty lost the Mandate of Heaven, so they would inflate the size of the bad last emperor's army. Ancient historians often wrote not to tell what happened, but with a specific moral purpose. So they didn't have the same scruples about bending facts to fit their story. Brant Gardner even discussed how one set of deaths in The Book of Mormon followed a same double same double pattern. (Alma 2:19) This could be a coincidence, or it had some sort of symbolic power. This is similar to the modern "I've told you a million times" or Jesus using the phrase "seven times seventy." So if The Book of Mormon has the same problem listing exact number for deaths on battle or the size of armies, as other historical documents this puts it in good company.
This gets even more confusing because some ancient words stood for a number and a unit. But the size of that military unit could change. Centurion means one soldier of one hundred. But by the late Roman Empire, Centuries only had 80 people. Myriad is another ancient word that have this problem. So when I see "ten thousand" listed so often in Mormon chapter 6 I start to that is a unit name and not necessarily a number. For example, by the end of the American Civil War some units in Lee's Army of Northern Virginia had only a fraction of their normal strength. (They did this out of pride because units didn't want to retire their colors and consolidate.) So if a general is listed as having "his ten thousand" there is a strong chance this refers to a unit name rather than a number. It is discussed in a bit greater detail in the first two posts here: http://mormonwar.blogspot.com/search?q=ten+thousand
Further, I find it odd that Mormon would begin his war of survival with 30,000 soldiers. (Mormon 2:42) But after many years of defeats, defections, and the loss of their capital city and lands, he had 7 times that number in the final battle. (Just from a logistical point of view I have a problem with this increase.) But when you look at the MPR this supposedly sudden increase in size makes more sense. The Military Participation Ratio is a formula historians use to figure out army and population sizes and other items. Basically its how many soldiers a society can muster for war. The high limit is usually 15% of the population can be mobilized for war. (Though ancient Sparta could muster about 25%.) For example, historians estimate that the U.S. MPR for WWII was 12%. So 30,000 would be about 15% of 200,000. This is close to the number listed in the final battle. This being the number of the total population gains strength when we read Mormon 6:7. If you read it carefully it sure seems to suggest that the order of battle included women and children. Towards the end of any war a nation scrapes the bottom of the barrel to fill out their army.
So even if the numbers are exaggerated by Mormon, or translated as numbers instead of units by Smith, or if these were unit names that didn't exist at their full strength, or the total population it doesn't matter. Having a problem with numbers puts it in good historical company, and a 30,000 man army and an ethnic group numbering about a quarter million is believable. There is both internal evidence and historical precedence for each view. Keep in mind that the writers in The Book of Mormon often complained about being "almost surrounded." Alma 22:29 In Mosiah25:2-3 we read that the Nephites were only about a quarter of the population of the Lamanites. (There are other verses that suggest the Nephites were a political minority, as well as significant outside sources from Mesoamericanists that often describe a small political elite ruling a much larger population, but this is getting on another topic.)