Another admin rights problem with this experiment: If the following rights ARE NOT selected: User admin, Options, and Themes, and the following rights ARE selected: Manage all albums, Edit, Comment, Upload, View all, Overview, then the Comments don't show up.
It is this specific configuration that makes them disappear. The culprit seems to be if "Manage all albums" is selected. If it is not selected and the other rights are as above, then the comments appear, but there is an error message on the comments tab:
Notice: Undefined index: private in /home/mysite.com/zenphoto/zp-core/admin-comments.php on line 347
Notice: Undefined index: anon in /home/mysite.com/zenphoto/zp-core/admin-comments.php on line 348
Again, this message goes away and comments work fine if admin is given rights to everything. Haven't experimented with other configurations.