Per David's instructions, I tested my theme and plugins to see what was causing my bulk add/predefined choices button to not work (I just get a gray overlay, no box popping up).
It looks like I have two sources of conflict: my theme, which is Genesis (I get the error with both my child theme and with Genesis itself activated), and also the podcasting plugin I'm using (Blubrry PowerPress). The box doesn't work at all with Genesis or the child theme activated; it does work with the default theme as long as I don't activate Blubrry.
What shall I do now, please? Both of these are kind of critical to the continued working of my site. I can provide login info if needed, or if I should post on the Genesis forums, I can do that. I'm actually testing it on the dev site of the site having problems, because I can muck around more easily in that--theme and plugins are all the same, so I trust that is OK. It's having the same issue, anyway. I also checked on another site running a different Genesis child theme and the problem is occurring there as well.