My host support staff are helping, and they don't see any server problems.
I've let them in, and they can see that the mail does not leave the Newsletter module.
Mail to xxx.domain.com do go out and show up in the logs. Mail to other domains do not show up. There are no error reports, no mail in the the drop or badmail directories or in the queue directory.
From what they can see, the script is not firing the emails. I'll report this as a bug, if I can.