Several more questions are answered in the FEC discussion of the relevant sections. What seems to matter is "who directs the blogging?", "who pays for the hosting?" and "who pays for the equipment?". Unfortunately, the answers bring more questions.
Of the examples below, Weintraub's California Insider would be regulated as corporate-sponsored unless newspaper exemptions applied (not clear as it is not the newspaper's opinion he posts). If he moved the blog to an ISP he paid for, and published the same commentary, it would be exempt. Then again, if it is subject to the SJ Mercury's editorial control, it may still suffer from corporate contamination. Or not. What a mess.
Blogging from a work computer, even to a personal blog, seems to be regulated, since you are being paid for being at work and the workplace owns the computer and network. This makes regulatory sense (if not actual sense) since it would be hard to determine whether the blogging is personal or directed by the employer. In practice, however, this part of the rule is unenforceable without trawling log files, so long as the blog is hosted elsewhere.
Professors Volokh or Reynolds would be considered to be using work computers and/or work-owned internet access even though they are in an educational setting -- their computers are not "public", nor is the network. A personal laptop hooked into a publicly accessible Wi-Fi network might be exempt though.
Then again, the FEC seems to be muddling the whole issue of "computer" -- the blogging process is network distributed in nearly all (ALL??) cases, and we are not told what level of insidious corporate poison is required to run afoul of the rule.
The rule is badly drafted. It seems that the intent is to differentiate paid political speech from other political speech and to regulate only the former. If the idea is to prevent sham bloggers, blogola and corporate or union fronts, they should concentrate the rule on "direction and control" not connectivity and ownership. The Internet is too distributed for that to make any functional sense.