Just in terms of geology, you could search HN links from the past year and find lots of areas of ongoing research and disagreement, for instance about the make-

Just in terms of geology, you could search HN links from the past year and find lots of areas of ongoing research and disagreement, for instance about the make-up and structure of the earth's core. And if you broaden the idea of "how Earth works" to include things like climate, then the number of areas of ongoing research becomes quite vast.