There are no security problems. If two people share an email account, and one of them has an account on your site, either of them can reset the password on the account (since they both have access to the place where the "forgot username" and "forgot password" emails get sent). Both people have the ability to take control of the account, and that's their problem.
The only concerns are usability. We have 3 types of email accounts:
One site user / one email user: In either case, they are unaffected. Even if you have to support specialized emails (recover username for email with multiple accounts), a regular user will still get the same email with just their one username.
One site user / multiple email users: Again, unaffected in either case.
Multiple site users / multiple email users: If you don't support multiple accounts, only one user can have an account, so half the people will be in the above group and half of them will be unable to create an account (or if they really want to, they will probably create a throw-away account they will immediately lose).
If you do support multiple accounts, this group will need a special "Recover username" feature that sends all the usernames attached to the account, instead of just one. So recovering a username will be slightly less usable because they have to figure out which username is theirs, but significantly more usable because otherwise half of them can't create an account in the first place. In the (unlikely) scenario that both try to reset passwords close enough in time that they can't tell which email is for whom (say, within the same day), it does fall on the users to figure it out by re-requesting a password change email one at a time. But again, this only affects this subset of users, half of whom would not be able to have an account in the first place.
So, I don't think there is any UX reason to prevent multiple users for one email address. The only cost is the additional development time, which should be insignificant or very minor.