I'm using the stock 1.5 Windows binary distribution; however, because the installation is executing on a Windows 7 64-bit target (QTIFW-514), the script was customized to ensure the default installation target was in "\Program Files", i.e.:

function Component()
{
    if (installer.value("os") === "win") {
        // <ApplicationsDir> maps to "C:\Program Files (x86)" if the installer
        // is 32-bit; so change.
        var appDir = installer.environmentVariable("ProgramW6432");
        if (appDir !== "") {
            installer.setValue("TargetDir", appDir + "/TheApp")
        }
    }
}

It appears that this causes the elevation pop-up to appear before installation (which is not surprising, given the target directory); however, this also causes "Execute" operations to fail.

E.g.: I tried with a simple batch script:

Component.prototype.createOperations = function()
{
    // Call default to extract from archive.
    component.createOperations();

    if (installer.value("os") === "win") {
        component.addOperation("Execute",
                               "@TargetDir@/test.cmd");
    }
}

This fails with the dreaded "Process failed to start: The parameter is incorrect." error. Using addElevatedOperation() (or setting <RequiresAdminRights>) made no difference.

Reading through similar issues, QTIFW-310 suggests adding a command argument to the Execute call, and this DID fix the issue. So it may be that they originate from the same underlying bug; but I thought it better to document the different cause.

If the @TargetDir@ is set to point to a 'user' location, the dummy Execute parameter does not appear to be required.