Blogging is dangerous for non-tenured faculty: Blogging will not get you tenure. Neither will giving talks worldwide. Tenure is usually granted because you were able to hold a decent research program, and you showed respect for the students. However, if blogging prevents you from getting tenure, something is very wrong with your blogging or your school. I have heard stories of famous bloggers who did not get tenure. But I have not been convinced that they were denied tenure because of their blogging. For my tenure case, blogging was a one-liner in my activity report. I doubt my colleagues paid any attention to it. Certainly, none of them had read my blog. But even if they had read my blog, I doubt if they would have found it very surprising. My blogging activities just reflect who I am.
Serious researchers have no time for blogging: Indeed, there is always another paper to write and more time to spend at the library, isn’t there? Let me quote Downes on this: If you are spending time in meetings, spending time traveling or commuting to work, spending time reading books and magazines, spending time telephoning people (or worse, on hold, or playing phone tag) then you are wasting time that you could be spending connecting to people online.
Blogging distracts you away from the research: bloggers do not tend to write about their latest research results. We tend to write about ideas that will not make it into our research papers. Is it a distraction? It might be, but does blogging cause you to lose focus in your research? I doubt it. If your research is out-of-focus and going nowhere, blogging may not help you, but you should not blame blogging either. However, your blog will help you write and communicate better. While a blog will not directly promote your research, the increased visibility it generates cannot hurt you.
Disclaimer: I do not claim that maintaining a blog helps your academic career.
Update: David Eppstein points out that if you get comments telling you that you are coming across in an unflattering light, it might be worthwhile paying attention to them.