But after installing a driver for an old mouse, I needed to reboot, and received that dialog Why would I get such a message?

Before installing mac OS Sierra, uninstall or disable any antivirus software on your Mac, as that may be causing issues.
Press the power button on your machine while holding down the Shift key on your keyboard.
) A few days ago there was a post on Mac Enterprise about issues setting Sierra’s login wallpaper.
I immediately posted as I had not seen the issues that were described, but after doing a deep dive last night, it is true - there are some changes to this functionality.
The new mac OS Sierra update is now available to download and install for OS X 10.11 El Capitan users, but if you've just decked out your Mac with the latest operating system and noticed that things don't work the way they should, or encounter any other issues, then we have a list of fixes for the most common problems.
As more of us upgrade to mac OS Sierra, more problems are being discovered, so we will be constantly updating this guide as new problems - and solutions - are found.
Boot your Mac into Safe mode, then try installing mac OS Sierra again.
It might also be worth switching from a Wi-Fi connection to a wired connection before you download and install.
Update 4: Note about non-blurred wallpapers and extra EFI data Update 3: Now with further management tools/discoveries.
Update 2: Now with safer methodology (Thanks Michael Lynn/Frogor) Update 1: Now with fix (Thanks Owen for inspiration!
You may not be able to determine this with certainty until you troubleshoot.