There is a new indicator on the user information screen - next to the email, which indicates problems with the email. The hazard symbol will be yellow if the email has bounced within the last 6 months. It will be red if the email has been blocked, which means no further emails will be sent. You can click the icon for details. The details are slightly cryptic since they are the exact information sent back, but you will find the reason for the bounce in there.
In the future, we will expand this functionality to indicate issues with emails on other screens.