Would it be worthwhile (given the added complexity) to vote on different aspects of posts, so it has seperately reported karma scores for correctness, being interesting, being a good approach, being useful, being entertaining, ect?

I would support a more complex karma system like that, and I think you've got a reasonable set of categories.

I'm assuming it would be grafted onto the old system, so that old karma score would be retained, but the more specific scores would be the only ones which could be added.

"Interesting" and "entertaining" karma shouldn't count for getting permission to do top level posts.