OK, I got a response to my support ticket, which seems to have resolved the problem of all comments needing to be approved before they appeared. I needed to delete the following old MT Blacklist files:

extlib/jayallen/*.* (three .pm files)
plugins/Blacklist.pl

Note that the second file is in the plugins directory, not the Blacklist subdirectory from there, which you create when you install the MTB plugin. Hope this helps anyone else who may be experiencing this problem.