I think it valuable to distinguish between bad writing and writing that deals with bad things. That's content. Bad writing is also presentation: a lack of care for words, for rules, for the readers.
Or bad writing can be beautiful and technically good but push for a bad thing. My example of this last type of bad writing is Javert's song "Stars" in Les Miserables--it is beautiful and sounds inspiring, but it is built around pride and a hateful vision of others.
I think there has to be some level of bad intentions in writing for it to be called bad--just making mistakes doesn't make one a bad writer. Perhaps I need to re-vision what I call "bad" (is "poor" just a synonym?) and reserve it for extreme cases, even as good seems to have a specialized meaning. At last there is Hamlet, with whom I don't quite agree, but find useful: "There is nothing either good or bad, but thinking makes it so."