"some customers have been sent an outstanding balance notification in error"
I know that, where email is concerned, it is really easy to fuck up even when you're trying to do things right.
However, it must be said that it would make things simpler if you could compare the recipients actually generated to the list you're expecting before sending out the mailing.
I do not know of any tool that allows you to do that. Of course, you could use Word and generate the mails before sending them off to Outlook, but that is you doing the job. I'm thinking of something integrated in your mailing tool that does the job and flags any discrepancies before proposing to send it all.