To answer the first question about what I think: I want to believe the gospel is true and sometimes I think that it's possible to separate the gospel from the church, but then...then I wonder how can or why would God restore a perfect teaching to people that are so imperfect, but then I remind myself that no one is perfect and I just kind of keep going back and forth. with it.
As far as exactly what the issues are, I only have a glimpse of all the things that have come up for dh. Some of them are the kinderhook plates, today he mentioned that throughout the BoM they talk about "church" when that's not even mentioned in the Bible once, some of Joseph's wives being so young and many already married, graduates from church institutions having their degrees revoked because of a change in their beliefs, the church building a mall in downtown Salt Lake (among other financial decisions)...that's just a few of the things he's brought up but it should give you an idea. Most of this is stuff that I already had an idea of, but now that's it's come to the surface, I kind of have to deal with it.