In the first place, I realise that you're probably going for an understatement, but I think it's worth noting that Rowling's world-building, in terms of thinking through consequences and implications, is actually atrocious rather than merely inferior. I'll never forget the moment when I realised that DISINTEGRATING LIVE KITTENS is standard spell practice for schoolchildren in the Potterverse, and no-one bats an eyelid. I sometimes ponder whether Rowling herself places an unnaturally low value on any form of life that can't speak a human language, or whether the themes evoked in the last books (that wizards are overdue to pay for their appalling record on non-human rights) are deliberately woven into the Potterverse at an extremely deep level.

That aside, could you give some examples of what you would consider such influences? Given that senior wizards in canon need to have guns explained to them, and that Muggle expert Arthur Weasley struggles to even pronounce "electricity", wizard obliviousness to Muggle society would seem to run so deep that I struggle to imagine one much influencing the other.