There are ten problems with the eleven witnesses and why they cannot be believed.
None of the witnesses should have been related to Joseph or each other. Most of the witnesses were either related or good friends. Having unrelated people as witnesses would be far more effective than using your brothers and father.
The witnesses should not have already been eager believers. There should have been some skeptics.
There should have been no financial motive. Martin Harris mortgaged his farm and invested some $5,000 of his own money into printing the Book of Mormon, so of course he had incentive to ‘promote’ the book.
Each of the witnesses should each have written their own testimony instead of merely signing a prepared statement written by Joseph. If the prepared document wasn’t 100% accurate many people would simply sign it anyway as it would be too much of a hassle to have it completely rewritten by hand - especially in the 1800s.
The witnesses should have been much more detailed about this amazing event. What did the angel look like? What exactly did he say? How did he speak? There are almost no details provided which can be analyzed and compared. If each witness had simply written their own account and provided significant details then their individual testimonies could corroborate each other.
The witnesses should have been interviewed independently immediately after going public. They should have been interviewed the same way police do with witnesses to crimes or that investigators do with UFO cases. Ask questions to see if their stories match; How was the angel dressed? How tall was he? How did he speak?, etc.
The witnesses should not have used subjective language and say strange things like comparing seeing the plates with seeing a city through a mountain or using spiritual eyes instead of their natural eyes to view physical plates
The witnesses should not have been gullible people that believed in things like ‘second sight’, divining rods, finding treasure by placing a rock in a hat, etc. That the Three Witnesses were a gullible sort is illustrated by an incident in July, 1837. Joseph had left on a five-week missionary tour to Canada, only to find on his return that all three of the Witnesses had joined a faction opposing him. This faction rallied around a young girl who claimed to be a seeress by virtue of a black stone in which she read the future. David Whitmer, Martin Harris, and Oliver Cowdery all pledged her their loyalty, and Frederick G. Williams, formerly Joseph’s First Counselor, became her scribe. The girl seeress would dance herself into a state of exhaustion, fall to the floor, and burst forth with revelations. (See Lucy Smith: Biographical Sketches, pp. 211-213).
All of the witness should have been much more vocal and been interviewed much more often. There are very few interviews done with the witnesses that provide any additional information or corroboration of their statements. You would think that these people, after seeing such a magnificent sight, would spend their time testifying to the world about their experience instead of largely just signing a prepared statement and avoiding interviews by the media.
And of course it would have helped had all the witnesses remained loyal to the Church for the rest of their lives instead of having most of them abandon it later on. It doesn’t make much sense to leave the true Church of God if you have really received an indisputable witness that it was true.
AMEN