In order to be as fair as possible to Nielsen, because I really have no beef with him, I will share the following quote from
How the Book of Mormon Came to Pass about the 1850 library census and its copy of Kircher as it relates to the possibility that John Smith had access to
Oedipus Aegyptiacus:
Incidently, the copy of Oedipus Aegyptiacus that the Rauner Special Collections Library currently owns was brought to America no earlier than 1795 [my comment: Nielsen is here letting us know that the book was available in America in Smith's lifetime] according to its small plate for John, English & Foreign Bookseller. It was unarchived, inventories, and made accessible to researchers for the first time in 1993. Interestingly, however, Oedipus Aegyptiacus did not appear in the 1809 catalogue when Dartmouth College produced its first inventory immediately after Professor Smith passed away. Neither does the title appear in the 1815 catalogue. Unfortunately, Dartmouth historians had lost track of the provenance of such rare books (some records were apparently stolen while others were consumed by a fire), which is why they were delighted to receive from me the evidence that I now provide in Figure 36. A census of the New England libraries was conducted during the 1840s and was published by the Dallas Theological Seminary in 1850. Therein, Oedipus Aegyptiacus was especially listed as one of the library's more precious resources. It may be that other New England professors mistakenly assumed that the book belonged to Dartmouth when in reality Professor Smith retained ownership, which would explain why it appeared in the census but not in the catalogues.
So, obviously Nielsen is very open about the problem of the catalogues. This is not dishonesty but it is a real stretch. What would need to happen here, if it is worth it at all, and I kind of doubt it is, but someone would need to find out what happened to John Smith's personal library when he passed away. That should not be such a tall order, but I think it may be beyond Nielsen's expertise and resources. I am not saying he couldn't figure it out. The question is whether he will invest the time in figuring it out. Honestly, I do think this is the kind of thing he ought to do, given the fact that he has presented this book as a challenge to LDS testimonies.
I don't see anything here that should challenge LDS testimonies. To the contrary, I am more than a little indignant that people are presenting such stuff as grounds for disbelieving their LDS testimonies. When one considers how consequential a high-demand religion is to the life of the believer, it should enjoin upon the person who seeks to get them out of it a sense of moral responsibility, in my opinion. When making the attempt, only credible, verifiable information should be used. I would say that the evidence of the Book of Mormon's 19th century origins is pretty well established. So, certainly, that evidence could be ethically shared as a reason not to accept LDS faith claims.
This book's highly speculative and conspiratorial hypothesis, however, does not come close to clearing the bar for credible or verifiable. Honestly, I don't know what Nielsen was thinking. Perhaps he drank his own Kool Aid. All I see in this book is a comparison of Kircher and Joseph Smith, Jr. that makes you go "Hmmm." I have absolutely no doubt that Kircher's views were sufficiently influential to inform Joseph Smith's ideas about things Egyptian, but I don't see any evidence presented here that persuades me that there was any kind of direct exposure to Kircher.
If we expect LDS apologists to be honest in what they do, then we should hold everyone in the conversation to the same standard. If we do not, then we have to confess that to us the end justifies the means, and we have no right to savage the Brian Haleses and Kerry Muhlsteins of the world when they fudge for the Lord. We would be fudging for what exactly? The higher truth? Hmmm.