The [systemtray] message has been removed. I am thinking that the BadWindow errors may actually be caused by Qt, as Trinity uses XClearArea very sparingly and you just helped rule out the only section of code that could have been causing the repeating BadWindow errors.
I don't pretend to be a developer, but that seems to make sense only from the amount of those messages seen. As I mentioned previously, I see the messages only with KDE and not Xfce or window managers. That indicates something peculiar to KDE/Qt.
Qt probably needs patching eventually. At least, that is the opinion of a few people who questioned whether proceeding with updating 3.5.10 is worthwhile. If patching is required then sounds like a project for 3.5.13 and not 3.5.12?