These "BadWindow" errors tend show in terminal when exiting KDE. There are multiples of them, and I'm not bothering to copy over the exact "opcodes" because it seems like everybody gets these, and I'm sure most users have seen them before.

I have been unable to find a cause or solution, though. I looked all over the Internet and here. People who have virtual terminals open on their desktops also see them when they close various applications. But I even see this if I just "startx" and then log out of KDE after it's done loading. It seems this even happens under GNOME and other desktops! Someone mentioned they wondered about the possibity of a "race condition".

Has anyone ever definitively figured this out? If so, how do I get rid of these?

In most cases, that is simply the result of the X server shutting down while applications where still drawing their windows. Everyone gets these "errors", and are nothing that you need to worry about or try and resolve.

There is really no practical way to fix the problem in the first place, it is just the way things are done in the Unix world. As the GUI is a separate entity from the rest of the OS (unlike Windows, for example) no assumptions are made as to whether or not a particular application needs the GUI when the X server is shut down. So some programs might not exit cleanly and give an X error, while others may continue operating without even being aware that X has gone down.