Apart from obvious fake emails, you should keep a lookout for spam emails. A spam email is an address either being used as a honeypot for spam emails, or one that is being used by spammers for other purposes.
On a daily basis we collect email addresses that are used for spam and other nefarious purposes, and blacklist them in our database. From a sending standpoint, you too should be concerned about these addresses, as their accounts are often on big domains like hotmail/yahoo/gmail and are regularly deleted, which means your deliverability will drop and with it your sending reputation.