James records its general email processing info for received and sent email in mailet-<date and time>.log, found at /usr/local/sourceforge/james/james-<version>/apps/james/logs/.
For a general overview of the email processing, this is the log to check.
If you are fielding reports from users claiming that they are sending mail to SourceForge and the email is not showing up in the application, you should start your troubleshooting here as this log will show if the user's mail server is even attempting to connect to James to deliver the email.