We write on the log whenever there's a situation that might requires future analysis. if you activate the WP_DEBUG constant, we write even more information to the log. I don't think this is going to change. What we could do is to prevent the html and text field to appear in the log.
If you use wp_mail to send you email, and you have activated the wpMandrill plugin, it will try to send your message no matter what. It implies that if for some reason Mandrill can't send your message, it will defaults back to the original wp_mail function. Returns false or failure is not an option for many reasons. We might add a flag to prevent this behavior if we got more request about this.
In the meantime, to prevent this to happen don't use wp_mail... use wpMandrill::mail instead. It will return a catchable error (actually, a WP_Error).