The various methods of handling distribution groups, shared mailboxes and alias email addresses are all discussed here.
Distribution Group Problems
Distribution Group Email Refused By CanIt
If you are seeing mail being rejected for Distribution Groups it is likely that you are using LDAP to generate streams. Distribution Groups are not defined within LDAP in a manner that CanIt recognizes as an actual user. This is discussed in depth here.
External Mail Blocked for Distribution Groups (Exchange)
Exchange 2007/2010 distribution groups by default only allow internal mail.
Open Properties->Mail Flow->Settings,
Message delivery restrictions-> Properties,
Uncheck "Require that all senders are authenticated".