I sometimes come across badly formatted or unclear questions when reviewing new posts. I usually flag those, but not all flags are accepted possibly because they aren't bad enough. That's why I use the down vote button as well. Note that I never down vote because some question is not interesting or not up my league. So, in some sense I find this button useful.

Maybe a reason could be attached to the down vote button, such as [Unclear, Off-topic, Spam, Whatever, ...] as some form of lightweight flagging system. Lobste.rs uses this on comments. Users that can't select a 'Not interesting' option are probably less likely to vote down.