Some of the errors include:
1) Separating oxygen from nitrogen is quite commonly done, and there are at least three distinct methods for doing it. The reference is to an amateurish analysis done by others who had not done any research. Source: http://en.wikipedia.org/wiki/Pressure_swing_adsorption
2) It is quite well known that NASA distributes its contracts around the country, so as to increase political buy-in from governors, congressmen, and senators. In fact, the space shuttle was green-lit because Nixon had cancelled the national aerospace plane, and his administration had a meeting about how that would affect votes in key swing-states, and they decided that the shuttle would benefit his re-election effort. Sources are numerous including https://www.youtube.com/watch?v=Fo8v7juSgRw .
3) Vitamin D would be a problem from lack of sunlight, not vitamin A, and even then supplements and artificial lamps both provide viable long-term alternatives to sun-exposure.
4) Building a vehicle to carry sufficient fuel and supplies for the trip to Mars is not especially technically challenging, when compared to the design of an earth-entry vehicle. Earth orbit rendezvous allows for the assembly of massive (though expensive) space vehicles such as the ISS.