Is the mail_logger module safe for production?
No, it doesn't enable any developer backdoor features (e.g. arbitrary PHP execution, code/stack dumps, etc.) if that's your concern. 

For the most part, its code base is Views integration &amp; an admin interface wrapped around its core function; intercepting outgoing mail through hook_mail_alter() and storing in the mail_logger table.

I'd say the only concern there is privacy for your users.