Basically Dan Vogel does not believe in any type of supernatural experience so it all must be false. He’s an atheist and doesn't believe in Jesus anymore than he believes in Joseph Smith. He tries to explain the witnesses all away by calling their experience just their 'imagination' and group hypnosis. He takes the different stories and try to show inconsistencies.
As an example his first point is that Martin saw his vision separately from David Whitmer and Oliver Cowdery.
The story is that all 4 went together into the woods and knelt down to pray but nothing happen. Martin decided it was his fault because of his unbelief. So he stepped away and the others continued in prayer and the Angel appeared to them. When that vision was over Joseph went looking for Martin and found him kneeling in prayer seeking the faith he needed. Joseph joined him and he too saw the same vision the other saw.
Now somehow because this is not written into the testimony of the three witnesses it makes it false. No reason is given that it makes it false just that the story is not there. And how does group hypnosis work like that?
He then tries to take their accounts and read into them more than what is there, it’s called repackaging. We see it today with all political spinning going on. People have been doing this from the beginning, it’s not new.
Martin Harris was Joseph Smith’s first scribe, but until he saw the Angel he never saw the plates. He was always behind a curtain or they were covered. He did however move them around, he said,
“I hefted the plates many times, and should think they weighed forty or fifty pounds.”
William Smith Joseph’s youngest brother and 16 at the time never saw them. However he says he felt them through a cloth and they were 60 lb. He said he could feel the leaves and the rings running through the back.
There were at the time a lot of rumors and misconceptions by outsiders, because one or two people miss quoted the witnesses it does not discount their witness.
Here’s an odd point, David Whitmer never handled the plates, while he saw them he never touched them. Oliver and Martin both handled them at different times as they were working as scribes and the 8 other witness also held them and turned the leaves.
Now if you want to have a real technical explanation you can go here and read Richard Lloyd Anderson answer to Vogal.
http://publications.mi.byu.edu/fullscreen/?pub=1399&index=4