There is no way to check whether email has been sent to an Inbox or Junkmail. In 95% of cases, especially if you haven't changed web hosts, etc., ListMail should ensure your messages are sent to the server correctly. If you're not sure, enable the SMTP Debug log by checking the box on the Send Email page or uncommenting the "$smtp_debug = 1;" line in admin.php (In recent versions, make sure your mail/attach folder is CHMOD 777 for writing) Check the text file log in the attach folder to see if there are any reported errors ListMail isn't picking up on.
After ListMail queues your messages to the server it's up to your host to ultimately deliver the email. One thing to note is that shared hosts are commonly temporarily or permanently blocked due to spam complaints against your, or other users on the servers', list email. This can cause delays or even temporary undelivery / bouncing of messages and is the bane of every list email publisher.
It is a good idea to enable "notify when a user is removed for bouncing" as a portion of the receiving server's actual bounce message is included in the notification. This can tell you whether or not a user was incorrectly removed for bouncing during a temporary or extended block/blacklist.
If you have trouble delivering to AOL, talk to your web host. With one phone call to the AOL postmaster hotline (
http://postmaster.aol.com) your server can be unblocked (for a while:)
Regards, DW