Mayday mayday... We are on 184.108.40.206 - Noticing when we create an order via magento admin, enter ship too, bill too, items, authorize.net CC info, and select shipping carrier and service, and complete the order; ALL shipping options go blank and the transaction posts and the CC is charged minus the shipping. Go back to the order details, and 'no shippng was selected' appears.
Do you see any logs either in your var/log/system.log or var/log/exception.log
Found the problem. Updating java script to the latest 8.65 fixed the issue. Seems then that the magento patch update alerts and downloads are an issue and conflict with other common programs such as java...
Follow up - the problem re-introduced itself and the java update is NOT the fix. Mozilla and internet explorer both do the same thing. Back to the drawing board...