From: http://en.wikipedia.org/wiki/Neutron_bomb
"A neutron bomb, technically referred to as an enhanced radiation weapon (ERW), is a type of
tactical nuclear weapon"
They're tactical weapons. You use them against concentrations of enemy troops, not to his strategic targets. Furthermore, you seem to hold the popular misconception that neutron bombs have no blast or heat effects associated with their use. This is not true, they merely have had their initial radiation effects boosted.
Neutron bombs would have dispersed enough initial radiation for five years, while general atomic bombs dissipate enough radiation for fallout to last only a year.
Citation needed. From what I know, 90% of fallout decays away in the first day. That's why its so dangerous, as faster decay means more particles emitted.
Of course, they would be used, especially on urban centers and resources, like mines, factories and refineries.
Prevailing nuclear doctrine is counter-force, not counter-value. Sites like that would never be targeted. Not to mention that even if one were to target them, you would never use tactical nuclear weapons. You would instead use airbursts to eliminate such "soft" targets.
After the scarcity of resources that led to the Great War why would you use only atomic bombs universally when you have neutron bombs at your disposal that would eliminate resistance while not destroying what you need? I think neutron bombs being dropped rather than atomic bombs makes up for the inconsistency of "bombs being dropped" yet there only being one crater and structures still lying around in the DC Wasteland.
You're not using those resources, this is nuclear war. No state is surviving this exchange.
Structures could easily remain, as I see no reason to groundburst the DC area.
However, it is possible when you combine the large amounts of radiation from neutron bombs and the rush of particles rustled up by the atomic bombs, that the half-life of the heated particles would last for five years and would then spread across the globe.
Citation needed. Could you explain how this would work, I don't know how this could extend the half-life of a radioactive particle. Keep in mind that neutron bombs do not yield higher amounts of fallout, just higher amounts of initial radiation.