According to our instructions "How to Upgrade to VaultWiki 4" which is linked from the site's forum home page and in a warning in VaultWiki 4's upgrade manual, VaultWiki 3 must be disabled in vBulletin's Product Manager when you run the upgrade process or VaultWiki 3 will interfere with the upgrade/install script.
You can re-enable VaultWiki 3 after installation is complete, but it is not compatible with the install/upgrade script (for the same reason VaultWiki 3 was not compatible with Tapatalk). This was a design flaw in VaultWiki 3 and unfortunately, there is not a way to handle this automatically from VaultWiki 4 without requiring some kind of admin intervention (install a patch on VaultWiki 3 first, etc). The simplest solution is just to have it disabled while VaultWiki 4 installs.
You will continue to receive fatal errors on some pages even though VaultWiki 4 has not finished installing, because vBulletin automatically executes some files if they exist in certain directories. The fatal error occurs because VaultWiki 4 is not actually installed, but vBulletin found the files and wants to run them.
Once you disable VaultWiki 3, return to the install script and click "Continue." When the installation is complete, you can re-enable VaultWiki 3.
I will leave this report open for now, because since refactoring the install script in the middle Betas, it might now be possible to write a work around for this issue within the install script. I'm not sure.