to unterstand when a certificate is valid:
you have a number of predefined certificate authorities (verisign for example) already included in firefox.
to get a valid certificate for your server, one of them has to sign it. when a client connects to your server, he gets the certificate and can verify the signature and thereby its issuer. if that issuer is trusted, the server can be trusted, and the client can initiate a secure channel using the public key included in the certificate.
now if you do not want to pay for a commercial certificate, you can create your own certificate authority. then you create a certificate signed by yourself. therefore zimbra fills the "issued by" field with your server name and "Zimbra Collaboration Suite".
that is what zimbra does by default.
if you want this self-signed certificate to be trusted by a client, it has to import your certificate authority (ca.crt) as trusted authority.
do you have a faculty certificate signed by a third-party (like your university or verisign etc.)?
then you have to replace the self-signed with this certificate.
when i open your server page (webmail.etf.unsa.ba), i see the self-signed certificate. furthermore it is issued to "igman.etf.unsa.ba", which will result in a warning ("wrong site"). the certificate is only valid for this name!
afaik, you cannot use multiple dns names with one certificate.
hope i could help