"The witnesses, by their own admission, seemed to have only seen the angel and plates in a 'visionary state' in their minds as Joseph suggested to them and not really with their natural eyes as members are taught. Why would real, metal plates need to be seen in a vision or with 'spiritual eyes' as many of the witnesses later testified"(mormonthink).
Some of the better rebuttals can be found here(Roper, Anderson, Peterson). I refer the reader to the links I've provided; this post will be short and sweet. The biggest controversy seems to stand around some later testimonies by individual witnesses referring to seeing with "spiritual eyes" or "the eye of faith". Critics will say that these terms refer to imagination or tricks of the mind.
This fatal misinterpretation is caused by taking these terms outside of their original Mormon context. For example, when Catholics say "sacrament", they mean ordinances. When Mormons say "sacrament", we mean the Lord's Supper. When Evangelicals say "saved" they mean not burning in hell, going straight to heaven. When Mormons refer to being "saved" we mean multiple things, such as being resurrected or even godhood. When critics say spirit, they mean the immaterial or non-existent; when Mormons say spirit they mean refined matter(D&C 131:7).
Martin Harris and David Whitmer are nineteenth century Mormons, therefore looking at how nineteenth century
Mormon texts use the terms "spiritual eyes" and "eyes of faith" will help us understand what the witnesses meant by these terms, better than retrofitting of a modern, non-Mormon, usage of these terms ever could.
"But now mine own eyes have beheld God; but not my natural, but my spiritual eyes, for my natural eyes could not have beheld; for I should have withered and died in his presence; but his glory was upon me; and I beheld his face, for I was transfigured before him"(Moses 1:11).
Eyes of Faith
"And there were many whose faith was so exceedingly strong, even before Christ came, who could not be kept from within the veil, but truly saw with their eyes the things which they had beheld with an eye of faith, and they were glad"(Ether 12:19).
Notice that these terms, "spiritual eyes" and "eyes of faith" are not replacements for actual seeing with the eyeballs nor is imagination implied. Faith and transfiguration are requirements for seeing these sacred objects,angels and Gods; they are not replacements for actual seeing, with the eye balls.
Like Moses and the brother of Jared, the witnesses were permitted to see because they first believed in the Book of Mormon and acted on that belief. By way of scribing for, financing and sheltering the Prophet and his translation, before seeing the plates or the angel, they "faithed" thus qualifying for knowledge.
As nineteenth century Mormons, David Whitmer and Martin Harris used these terms in the way nineteenth century Mormon texts use them, not the way twenty first century secular humanists or evangelicals do.