As an addition to uxbod's details: I have several domains pointing to one server, some with just the MX entry and one or two with an A record too, and it works fine.
Having the A record point there has the advantage of users being able to login using just the name part of their address (rather than name@domain). It also helps you if you have reason to try to keep services visibly separate (so company2 doesn't go to
http://zimbra.
company1.com to get their mail and calendar, for instance).
On disadvantage of using the A records is present if you use HTTPS with a not-self-signed certificate - only one domain can have the valid certificate
[unless Zimbra can be easily convinced to operate on multiple IP addresses and associate each address with a specific domain with it's own certificate].
In short: just the MX record will work fine. Adding the A record goes a little way to keeping up appeareces but isn't important other than that.