There is a 50 hourly email limit per domain, this limit is also applied towards mailman. If you send over this amount in any hour most of the e-mails will bounce back with a undeliverable error.
Many of our servers have a 60 pop checks per hour limit per domain. If you go over this you're likely to get a wrong password error message saying login incorrect. Just wait an hour and it will automatically unlock you. To prevent this from happening again make sure to disable auto checking or at least set it to something higher such as 10 minutes.
Any mailing list larger than 5,000 will require a VPS or dedicated hosting solution from us.