How can I determine when the last time a specific computer requested (or checked for) a policy update from the NS without checking the agent on the client computer itself?
ITMS 7.x, 8.x
You can check a single asset by just right-clicking on it in NS and selecting Resource Manager. In the Summaries tab you can then drill down to Resource Manager > Resource Summary, and then in the right pane under Altiris Agent Details, you will see when the agent was First discovered, Last Configuration Requested, Last Inventory Received and Last Event Received times.
For a fleet wide inventory report, go to the "Reports" tab in the SMP Server Console and under Notification Server Management > Agent > Computer last information update time you will see how long the systems have been since last time its information has been updated.