Blogging is not (necessarily or probably) scholarship. Who cares? That doesn't mean it shouldn't count.
There was a great session at the OAH (Organization of American Historians) annual conference last month on blogging and scholarship (summary, critique, and video, another summary and critique here, Ann Little's introductory remarks here). The general conclusion is no, blogging isn't scholarship. For one thing, no peer review. So while it supports scholarship, it isn't itself worthy of consideration for tenure and promotion.
Blogging is certainly not scholarship for me. I blog about disability, criminal justice, gender, parenting, academia (teaching, adjuncts, admin, everything), politics, history, and writing. That's just the short list, really. My scholarship, on the other hand, focuses on Venice, relics, memory and the crusades. The Venn diagram appears to be two circles that don't touch, except when someone invokes medieval notions of militant Christianity in a speech to the NRA (or someone steals a relic).
For people who work on modern topics, the overlap between scholarly field and blogging can be much more direct, as it can be for people who only blog about their scholarly field. This is very much the case for the Americanists, in general, on that panel (I can't say I read all the American history blogs all the time). For me, however, because there's basically no connection between my scholarship and my blogging, how could blogging be scholarship?
Also, there is an absolutely tight connection between my blogging and my scholarship. I write about language. I write about memory. I write about epistemologies. I write about the words we say, the stories we tell, the ideas we shape and are shaped by. I argue that words and ideas matter, that they exist in a tight dialectical relationship with actions, that the objective reality of the world in which we live shapes the words and ideas that we use to describe them, and vice versa (that's the sometimes contested part, I suppose, for people who think language isn't that important).
When I blog, when I write about memory, language, or narrative, I am exercising the same intellectual muscles that I use to write books, articles, and lectures. Does that make blogging scholarship? Of course not. But blogging makes my scholarship better, it makes my scholarship more visible to a larger audience, and it's all one thing.
Blogging should be able to count for tenure and promotion. If we believe in public engagement, then public engagement should count. That was my answer to Kristof a month ago and it remains my answer. If we, The Academy, think public engagement matters, then it has to count. We cannot leave it for the tenured to do from the safety of their job security. We cannot hope people make irrational decisions to engage despite it not counting (and sometimes counting against it). We cannot cling to the norms by which we were judged in our pursuit of jobs, publications, and tenures. We can, instead, create new norms.
Those norms may differ wildly by field, but we will not lack for data. In normal assessment of scholarly merit, we rely on diffuse and inexact notions like "prestige." I can tell you precisely how many people have viewed my blog, have linked back to it, and see the spread of ideas in a way that is much more concrete than with traditional scholarly work. Yes, it can be gamed, but so can citation counts. We can come up with ways to measure this kind of thing.
The question of whether blogging should be considered scholarship is, as others have said, the wrong question. For me, the question is this: Does the blog contribute to a field of study? If yes, count it. If not, then not. Forget anonymous peer-review scholarship as the only kind of activity that matters.