About what fraction of downvotes have bad justifications? Is this a serious problem (measured on the level of importance of the karma system)? Is there anything that can be done about it?

It's just karma. Not a big deal.

My assertion of a norm was based on the idea that downvotes on lesswrong are often explained but usually not explained, and deviating from this fraction would bring, on average, less respect from the community, thus constituting a norm. I think the definitions of "often" and "norm" are general enough to make this statement true.

I was responding to "and there should be one of doing so more frequently". If you declare that the community should adopt a behaviour and I don't share your preference about the behaviour in question then I will downvote the assertion. Because I obviously prefer that people don't tell others to do things that I don't want others to be doing. In fact there is a fairly high bar on what 'should be a norm' claims I don't downvote. All else being equal I prefer people don't assert norms.