I've discovered I can downmod some comments (though I haven't yet), and not others. That gets me thinking about things like "What are the rules? At what point do I get the ability to downmod articles? Is it all relative to the karma other users have?"
. . . but it's just idle curiosity (for me, at least). The only time I've honestly, earnestly wished I had the power to downmod submissions was when the front page was full of the most banal possible Erlang articles, to the point that even good Erlang articles couldn't get to the front page. The rest of the time, the fact I lack the ability to downmod submissions just makes the place feel a lot more laid-back than other places, even while the fact I know the HN members with the most activity over the longest time can downmod submissions makes me feel better about the ability of the community to police itself than places that only allow upvotes for everyone.
I think, if I were to implement something like this, I'd probably try grading on the curve. Maybe the tenth percentile would be able to downmod comments, and the second percentile would be able to downmod submissions -- or vice versa. Maybe I'd make comment downmodding a privilege based on relative karma, and submission downmodding a percentil cut-off. I'm not sure. I'd want something that grew organically with the community, though, rather than eventually being 98% of the community because most people have been there long enough to have 200 points and the remainder are newbies and lurkers.
edit: That ended up being much longer than I expected (thanks to rambling off into speculation about what I'd do with a new discussion Webapp).
I believe that you can't downmod comments that are on a thread that you've responded to. This is to prevent pile-ons, where debates get so heated that people just downmod all opposing POVs that they don't agree with. Similarly, you can't downmod comments that are more than a day old from the user page, to prevent people from downmodding all comments of a person they don't like.
. . . unless it's more complex than it at first seems. I don't really have the LISP Fu yet to figure it out from the source.