Assuming you have a recent version of Zotero, that's a problem with your Firefox installation. Zotero is properly signed for use in Firefox. Redownload Zotero from the download page, and if that doesn't help try reinstalling Firefox.
I uninstalled Zotero for Firefox, and then restarted Firefox.
Zotero was then not found by Firefox's "about:addons" search.
When I tried to install from "https://www.zotero.org/download/", there was a warning: "Firefox prevented this site from asking you to install software on your computer". When I overrode that, it allowed me to install the add-on.
Odd; I've been on that version, and used Zotero with no problem, for a while.
Not sure which version you mean, but if you were on a much older version of Zotero and just upgraded to Firefox 48 (which requires signed add-ons), you'd get this message now. Otherwise, probably just a Firefox glitch.
Zotero was then not found by Firefox's "about:addons" search.
Yes, we don't distribute Zotero from the Mozilla add-ons site, because the review process doesn't work for an add-on for Zotero's size.
When I tried to install from "https://www.zotero.org/download/", there was a warning: "Firefox prevented this site from asking you to install software on your computer".
That's normal when installing any add-on from a non-Mozilla site.
I have Firefox 48.0.2. I tried to install Zotero from the zotero download site.
I had to do this after finding zotero no longer ran and "refreshed Firefox" (essentially a re-install of Firefox).
I overrode the "Firefox prevented this site from asking you to install software on your computer" but then Firefox came back with "www.zotero.org: Firefox has prevented this site from installing an unverified add-on." It then refers me to Add-on signing page of Firefox.
Now I can disable add-on signing completely apparently in about:config but I am not keen to do that. Are there any other solutions?
I have the same problem. I tried disabling add-on signing in about:config but it was ineffective - which is to be expected according to https://wiki.mozilla.org/Add-ons/Extension_Signing which says there is no way to work around add-on signing. This applies to both extensions (zotero firefox and the firefox extension for standalone)
Upgrade Storage
Just upgraded to FF 48.0.2, got the same message.
Zotero was then not found by Firefox's "about:addons" search.
When I tried to install from "https://www.zotero.org/download/", there was a warning: "Firefox prevented this site from asking you to install software on your computer". When I overrode that, it allowed me to install the add-on.
Firefox 48.0.1 - which I'd had pretty much since the day of its release, mid-August.
The version of Zotero I was using was also recent. I only installed it on this machine about a month ago (and the machine has been used daily, since).
I had to do this after finding zotero no longer ran and "refreshed Firefox" (essentially a re-install of Firefox).
I overrode the "Firefox prevented this site from asking you to install software on your computer" but then Firefox came back with "www.zotero.org: Firefox has prevented this site from installing an unverified add-on." It then refers me to Add-on signing page of Firefox.
Now I can disable add-on signing completely apparently in about:config but I am not keen to do that. Are there any other solutions?
https://wiki.mozilla.org/Add-ons/Extension_Signing
which says there is no way to work around add-on signing.
This applies to both extensions (zotero firefox and the firefox extension for standalone)
https://forums.zotero.org/discussion/59829/zotero-5-0-beta#latest
does work! with firefox 48.0.2.