If you're using POP3, all the message parsing happens on the client side in JavaMail. Have you looked at the many properties you can set in JavaMail to configure how parsing errors are handled?
If you're using IMAP, most of the parsing is done by the server. What sort of parsing errors are you still having with JavaMail? Are they problems parsing the content of the email messages, or problems parsing the IMAP protocol messages?
With more details of the problems you're running into, I might be able to help you configure JavaMail to work for you.
If you really want to use another MIME message parser, you'll need to use the Message.writeTo method to get the entire MIME content of a message, which you can pass to some other library to parse.