A major issue is that the moon is fairly far up Earth's gravity well. It is easy to get things to low-Earth orbit and already tough to get things to even geo-stationary. The main saving of putting anything on the moon will come if you can do a large part of your construction on-site since otherwise moving that much material up is going to be tough. If you are doing automated construction on site you also are going to need to be able to make mainly a lot of solar cells. Solar cells are primarily silicon and there's already been prior research on refining the moon's regolith for silicon to manufacture electronic components and that looks possibly doable but one does need to get over some technical chemistry issues. See e.g. http://www.asi.org/adb/02/13/02/silicon-production.html.
The other issue is distance for power transmission: most designs for microwave power involve power transmission from at most a little over geo-stat at about 35,000 km. The distance to the moon is about 10 times that, so if you don't have a really tight beam, there are going to be issues. Also, since the moon change's position you are going to need a large number of sites on Earth that can receive the beam, and if you can't switch off smoothly between them always (which would itself require massive planet-wide infrastructure), you would still need power sources on Earth (possibly just massive storage facilities?) to deal with those times.
Overall, a really cool idea with a lot of technical hurdles. I hope they can make it work but I'm not optimistic.
Nope, not really. The issue isn't his religion, it is that his religion by his own description motivates his conclusions and results. Not too long ago I was talking to an undergrad who said that he wanted to become a climate scientist because he wanted to get people to stop using fossil fuels. I told him that he should instead become an engineer.
The problem in a nutshell is that humans are deeply imperfect. So when we have external motivations, and those motivations are strong enough, they distort what we do. That can occur in a variety of ways such as the file drawer effect http://en.wikipedia.org/wiki/File_drawer_problem#File_drawer_effect but also more subtle issues. In this particular context, there are literally hundreds of predictions from the 1980s about what the climate would be like today. That means that there are very difficult decisions to make about which predictions one should compare to the current data, and how to measure how accurate they are. Spencer's own motivations make the decisions he makes there to be extremely problematic. And yes, science is universally reproducible, but we're not talking about whether to accept a specific paper in a journal (if we were climatologists who were doing so, I agree that Spencer's motivations should then not enter into that), we're talking about non-climatologists who have neither the full time nor full expertise to make a judgment about all the details of his claims. In that context, the fact that he has strong external motivation is highly relevant when scientists lacking that external bias by and large disagree with his conclusions.
"Survey says..." -- Richard Dawson, weenie, on "Family Feud"