Hi Patrick,
It looks like the customer's environment is missing some javascript files that are deployed during the QWP installation process.
I attach a screenshot of the files and the structure that he should see in his env. on all WFE servers where QWP are deployed.
Please note that this screenshot was taken from a QWP 5.7 SP2010 and the files can vary for different QWP and SP versions.
To fix the problem I'd suggest the customer to retract/deploy the QWP wsp solution and monitor the above files.
If that still doesn't fix the problem then ask then to contact Quest Support.