How to submit an error report to app developer?
Implementing the sending part of a mail client in AppleScript is probably rather a challenge, but there might be other means:


Use a mailto: scheme to launch the mail client the user is using. You won't be able to provide a mail template though (but you could prepare something in the clipboard and have the user paste it into the new mail), and it will fail for those users who don't use any mail client at all.
Create a web form on a web server of your choice and direct users to this site if they want to give feedback.
Collect user feedback within your application and just post it on your web server in the background.