Zotero typically works out of the box with the newest Firefox release. However, if you're testing Firefox releases from the Aurora or Beta channels, there may be some hoops to jump through to get Zotero working.
Warning: While the risk of data corruption is low, some or all Zotero functionality may be broken with Aurora and Beta Firefox releases.
Zotero 3.0 and later is compatible with Firefox 3.6-17.0 (and probably later versions as well).
The Zotero LibreOffice and Word for Mac plugins typically work with new Firefox updates. Depending on your configuration, you may need to install the Add-on Compatibility Reporter to force compatibility.
The Zotero Word for Windows plugin must be updated for each Firefox release. Compatibility may be available in the WinWord Integration Trunk XPI prior to release. Currently, Zotero Word for Windows plug-in version 3.1.6 supports Firefox 3.6-12.0.