I searched the Zotero support section and couldn't find any useful answers. Taking a second look at the Word Processor Plugin Installation page, I noticed some advice for when the Zotero options weren't displaying at all. This wasn't my problem, but I tried their suggestion for that issue and it worked.
In Firefox, go to Tools→Add-ons→Extensions→Zotero OpenOffice Integration→Preferences and click “Reinstall OpenOffice components”.
Now I had a new error message though:
Zotero OpenOffice Integration could not communicate with OpenOffice.org because the Java UNO runtime directory specified in the Zotero OpenOffice Integration preferences does not contain a “ridl.jar” file.
this page. I installed the package openoffice.org-java-common using synaptic package manager. Then I went back into Tools→Add-ons→Extensions→Zotero OpenOffice Integration→Preferences and clicked 'Detect OpenOffice.org paths'.