In Nevada and (I believe) under federal law you are disqualified from possessing firearms if you are in possession of a controlled substance. That is what makes Chumlee a prohibited person.
As for gun registration in Nevada, up until a year or so ago, we were required to register handguns if we resided in Clark or Washoe County. It was known as the Blue Card system. This was instituted in the 1960s, supposedly as a law enforcement measure. However, given who owned Vegas and Reno at the time, I think it was more for their benefit.
It is alleged that during the whole of its life, the Blue Card system was instrumental in solving one shooting crime.
The other gag with the system is that if ownership was transferred there was no way of returning your Blue Card and getting it off your name. California is the same, I believe. So, MANY handguns in the valley were "registered" to multiple people.