I've been wanting to get warnings on partial functions (and partial record accessors, while we're at it!) for some time.
And, I think it would be quite easy to have GHC infer partiality. As far as I can see, partiality can come from only two places: the use of a partial function, and an incomplete pattern match.
(I'm ignoring nontermination here, which I think is best considered separately.) Before getting this into GHC, though, we'd need to make sure the incomplete-pattern-match checker is up for it (see #3927), but that work is being done right now. And we'd definitely need a way for users to declare "This function is total! Really!"
I like the idea of user-specified warning categories, but I think partiality is easy enough for GHC to infer that it should be built in.