Thanks for the quick reply Kyle.
I'm afraid those changes didn't fix the problem. I've made sure that the plugin is public, created public test groups, made sure the categories are public, and created a public GJ menu item, but anyone below "Author" level access is told there are none available.
Registered users also cannot see GJ invites they've received, other than in their mailbox. Trying to access the (open) group through the message gives the message that the user is unauthorized, as does trying to accept the invite.
I'd prefer not to have to circumvent this by making all users authors (with accompanying reductions in access privileges elsewhere, of course). Is there something else that might resolve the problem?