e-newsletter quits after first bad email address

So I got e-newsletter all set up, and imported 13,000 email addresses. This was surprisingly fast. However, once I started a mailing, it stopped on the third email, saying the email address was bad.

Now, there will be bad email addresses. That's the nature of user-generated lists. I can't imagine this thing has been in production and it's been usable if it stops running on the first bad email address, so... what am I doing wrong? How can I fix this?