The Three Witnesses of the Book of Mormon. From left to right: Oliver Cowdery, David Whitmer, Martin Harris.
Among the reasons given are 1) many of the witnesses were related to or friend with Joseph Smith 2) some of the witnesses claimed to see the plates only in vision with a subjective "eye of faith" 3) at least one of the witnesses claimed to have also been told by God to leave the Church, which presents a dilemma for Mormons because that same witness is said to have received that commandment from the same God who testified to him of the Book of Mormon and 4) the Witnesses were superstitious or gullible into believing things of a supernatural nature.
It is beyond the scope of this post to ascertain the validity of all the arguments for or against the witnesses of the Book of Mormon. A considerable corpus of literature has been created on this subject, and the intrepid reader is to read some of those offers to see the different arguments on the two sides of this debate.
However, as a believing and active Latter-day Saint and after reading much of the aforementioned literature, it is my conviction that the witnesses to the Book of Mormon not only are reliable but that it is more parsimonious to believe in their testimony as it stands than in the theories of critics of the Book of Mormon.
For this post, I will therefore only focus on the offerings given on the website in question and will not focus on other specific criticisms by the likes of Dan Vogel or Grant Palmer.