I don't know what happened, this form has been working for months now. The only thing that I was tinkering with was alternate access mappings.
The form in question does a SaveAttachment and a SubmitToSharePoint list. The SaveAttachment works fine, but the SubmitToList is not submitting. Well, it is for ME, but not for everyone else.
I noticed something wierd in the list . . . the list entries that I submit are created by me, the created by column says my username. Previous entries (from last week) have system account as the created by person, even for my entries.
So it seems as if it is now trying to submit the list items as the logged in user, and they don't have rights to the list.