Hitler's anti-semitism (from memory) came from his sense of 'Jews' having simply too much monopoly of business - this sentiment formulating most in his student days.

The Rounding up of muggles and assigning part-muggles with an identification Number is as close to 'nazi' practise as you can hope to get. but I don't think the remainder of the Death Eater activities were directly nazi inspired as such.

Incidentally - the Lord of the Rings... I always like to imagine which countries Tolkien is referring to....
Hobbiton - rural england
Rohan - Sweden/Norway (viking imagery)
Gondor - makes me think of Russia
Mordor - again - only the axis of evil springs to mind. so, perhaps Germany - WWI and WWII.

the LOTR sentiments about environmentalism....
the Harry Potter sentiments about elf rights...
the WWII sentiments about basic equality regardless of race or religion.

so many interesting parallels I think