After investigation, I've submitted the following defect report to the development teams at Esri:
[#NIM092220 Operations Dashboard crashes on a Virtual Machine (VM) immediately after configuring the MAP widget.]
This is reproducible in multiple environments, the common theme is that this failure is only reported on virtual machines.
I'd be curious to know if anyone has been able to get past this crash on a VM, and if so, what flavor of virtualization technology is in place. I've tested using VMWare LabManager and with EC2 instances on the Amazon cloud (which use XEN).