I've wondered about the "something I know" dimension as well. Perhaps a passphrase could be used (it already is used to secure the master key). It'd still be a major improvement, as only your local device would need it, and you wouldn't have to have a separate password for each site.
(And no problem. If we were forced to comment using only precise terms, with no simplifications, comments would either be ridiculously long or nonexistent.)
Con: requires internet connectivity, unlike some 2-factor implementations
So, it seems feasible offline with online required only for convenience.
The example in the article being login at the library - the library computer has Internet access, but your phone has to also connect to a wifi (if there is one), or the mobile network (if you are 3G subscriber and there's reception). Then factor in that you might go abroad, I don't know many places where they just give free internet access to anyone with a smartphone...
He spends a good chunk of the latest episode of Security Now [1] describing it's advantages over current schemes. The episode isn't up yet (I listened to it on the the site's live stream), but it should be soon.
Whatever you use to unlock/authenticate to the device would be the other factor.