It seems that if you look at the column on the right of the page, you can see upvotes and downvotes separately for recent posts. The same [n, m] format is displayed for recent comments, but it doesn't seem to actually sync with the score displaying on the comment. This feature only seems available on the sidebar: looking at the actual comment or post doesn't give you this information.
Thanks, whoever did this!
It has always been explicitly possible to sort comments by controversy by clicking on "sort by." I believe that in the beginning there was a link to sort posts by controversy (discussion). At some point the link was removed, but the URL kept working. At some point I recall someone discovering it and people being suspicious that the sorting was buggy. But currently it lists posts that have received lots of upvotes and lots of downvotes. Added: read the rest of this thread for more detail about these links.
I haven't figured out what the definition of controversial is. There used to be a paragraph here speculating about it. I previously linked to the open thread, which was not a good example to exhibit sorting. The politics thread contains actually controversial comments and thus sorting actually does something.
As of now, the controversial posts page includes quite a few posts with 100% positive karma.