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.
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!