Mormonism in general can be a devastating anti-religious datum. Yes, the internet atheists try to point out the silliness of various aspects of religion via parody, but they're generally preaching to the choir, because their parodies are transparently too silly. "Kissing Hank's Ass", "The Flying Spaghetti Monster", etc. work as allegory but fail as persuasion.
But Mormonism? It's as if someone exaggerated the least plausible parts of many religions, but did so gradually enough and subtly enough that a significant fraction of a percent of the population really, truly believes it. If religious people are trying to tiptoe around landmines of irrationality and if you want to warn them about this, talking about the FSM is like showing them a crayon cartoon of an explosion, whereas talking about Mormonism is like showing them a gory video of a sympathetic victim.
But whereas exposing other religions to Mormonism (not just the Book of Mormon; you really need the whole context) can be enlightening, I think it's nearly worthless as an abstract rationalism-improving topic for LW. A room full of atheists is not the right venue for a wit-sharpening intense debate about any religion; what you'd probably get instead is a dogpile against anyone who took the minority view, interspersed with rounds of self-congratulation about how great our shooting skills must be to have hit nearly all the fish in that barrel.
If you're interested in irrational bits in the Book of Mormon for some concrete rather than abstract reason, on the other hand, you might as well skip ahead to the notes in the back of the book: Skeptic's Annotated Book of Mormon
LessWrong people generally don't have enough exposure to the LDS church or the Book of Mormon to have a reason to take it seriously, and their worldview is so different that it would be hard for them to even understand why Mormons take it seriously in the first place.
But as a former Mormon, who was born into the church and attended church almost every Sunday for at least 30 years, I'd like to summarize my journey (briefly, as this discussion died off long ago):
In this comment thread, I gave the following idea, on the topic of a method by which one might judge the Book of Mormon from a rationalist perspective:
I would appreciate feedback on this idea, for an admittedly selfish reason: I am trying to instigate in myself a Crisis of Faith. So, here are the questions I pose to you: