I put more information on SuperUser: http://superuser.com/questions/663232/java-app-misdraws-screen-on-dedica...
My other Java apps do not have this problem. Neither does my NetBeans 7.3.1 installation.
I've discovered the following documentation for NetBeans and tried the java JVM options specified there with no success.
The file that I inserted the options into was ireport.conf.
I just tested the same system with iReport 4.7.0 and discovered no issues with the Report Query window.