nslookup & dig fail; ping, traceroute, and scutil -r work
I'm still not sure what was causing the problem, but after suffering from another seemingly unrelated issue, I did a complete re-install of 10.8.  I had originally upgraded from 10.6 -- though the utilities had seemed to work fine for a while after the initial upgrade, my suspicion is that I did something to some unknown-to-me configuration while attempting to diagnose/resolve the other issue (something that apparently disabled some aspects of DNS access).

After the re-install, all DNS-related utilities are now working fine.