In all likelihood Zimbra is doing exactly what it's supposed to do. It is not supposed to accept SMTP mail for the outside world, FROM the outside world; to do so would have an open relay that would be spamming its brains out in no time.
To get this to work you need to set up "Enable authentication" and (preferably) also TLS. . .it's more secure. You also need to be sure that your Outlook client is authenticating on the same ports (remember secure authentication is not on the same ports as clear-text) and, depending on which you select, you also have to enable or disable clear text login. I strongly prefer disabling cleartext logins, and even authenticated logins on 110 and 25, preferring to stick with SSL for less hackability, but that is a choice you have to make.
This thread goes through the reasons that some people have had troubles with external authentication. There are at least two or three different problem/solution sets discussed there, any one of which may help you.
Failing that, you might try an external authentication session, and then post any lines in /var/log/zimbra.log that you find in association with the time of the failed login.
Cheers,
Dan