This issue is caused by the UI sending concurrent calls to power on/delete the virtual machines.
The first virtual machine powered on marks the vApp as busy which blocks additional virtual machines in the same vApp being powered on with the error, "busy completing an operation VAPP_DEPLOY".
To workaround the error vApps with multiple virtual machines can be started from the Data Centers, vApps or Applications, Virtual Applications sections of the Cloud Director Tenant portal.
Starting a vApp will cause all virtual machines within it to be powered on.