The logistics involved with Uranium separation on an industrial scale simply were impossible during the second half of WW2 for the Nazis - they did not have the materials or the expertise to construct enrichment / separation plants.
The theory nor materials were there to produce a Plutonium device either - no critical pile of any significant size was made, and as far as I know the understanding that a much smaller critical mass of Plutonium was needed was missed entirely as well.
The Nazi bomb program is a great example of the effects of a Scientific embargo - all of the powers at be at WW2 knew the US and UK were up to something involving radiation as most of the leading scientists in the field stopped publishing in the late 1930's until the conclusion of the war.
An interesting read on the subject is Heisenberg's War - http://www.amazon.com/Heisenbergs-War-Secret-History-German/...
https://www.amazon.com/Heisenbergs-War-Secret-History-German...