If you go to the membership management page for a Mailman mailing list, you will see a checkbox next to every member's address in a "mod" column and an option to "Set everyone's moderation bit, including those members not currently visible" near the bottom of the web page. If you check the mod checkbox next to the member's address, the list member will not be able to send messages to the list without the message being approved by the list owner or a moderator for the list.
When the box is checked for a member, postings from the member are held and administrators are notified of their existence. They may then approve or reject postings via the web interface. If unchecked postings to the list are immediately delivered to list membership.
If a list is to be used only for announcements from the list owner and designated moderators, then everyone else should have the box checked.
Note: Applies to Mailman 2.1.14 as well as other versions.