Zotero shouldn't try to self-update
Lately I've been bothered by Zotero giving me unsolicited advice about updating it. It says "Unable to Update; a recommended update is available, but you don't have permission to install it. To update automatically, modify the zotero program directory to be writeable by your user account." Even besides the fact that this message is an annoyance, programs shouldn't have to update themselves. Updating should be the responsibility of the package manager, not each individual program. Furthermore, the user shouldn't have access to system files. If I install Zotero to /usr/share/something, for instance, I shouldn't need to (or want to) modify that directory to be writeable by my user account--that would be a disaster. So long as Zotero packages are properly maintained in package manager repositories (I use the zotero-standalone package in the Arch User Repository) the program shouldn't ever have to tell the user to modify file permissions in order for Zotero to update itself, and it shouldn't have to tell the user to download a new version from zotero.org, since updates will come through the usual channels.
The standard mode of installing Zotero on Linux is to download the tarball and run the program directly, typically from a user-accessible location like ~/.local/bin
In that scenario, auto-updating is crucial.
Maybe Zotero should just consider packaging Zotero Standalone the normal way, through Linux package managers? Besides all the benefits I've already mentioned, another advantage is that you wouldn't have to repackage libraries. For example, if I have a program that uses some library, and then Zotero also uses that library, they can both use the same library, without having to distribute their own version of that library, which could be redundant.
Packaging for the various linux distros & flavors is a ton of work, which is why Zotero (like mozilla) has never done so, but there is an open ticket if people want to help adapt the deploy script: https://github.com/zotero/zotero-standalone-build/issues/52
I've just added a comment to the AUR package page about changing that preference--I'm assuming it's `pref("app.update.enabled", true);` to `false` in /usr/lib/zotero/defaults/preferences/prefs.js? I've also added an issue here about an Arch package: https://github.com/zotero/zotero-standalone-build/issues/57. Additionally, I just posted a comment about adding a line to the Linux installation readme: https://forums.zotero.org/discussion/63880/linux-installation-instructions-for-standalone