PROBLEM SOLVED - I HOPE !!
Rather than visit a Genius Bar, I opted to buy an inexpensive (<$40) external USB-connected CD/DVD reader/burner (Samsung SE-208AB). I discovered that it too exhibited the same problem whereby DVDs and CDs burned in the Finder failed verification almost as soon as it began. Even though the burned discs appeared OK in that the files/music/movies were as they should be.
In addition to all the steps taken above, I also used the Recovery Disk to re-install a copy of Mountain Lion in case something was messed up. To no avail, the problem persisted.
After much more searching I discovered a tip that I had not tried. Someone had found that deleting the Finder preference file resolved their problem, in 2008 no less. So with nothing to loose, I deleted the Finder preference file, restarted and burned 3 discs flawlessly. Attached below is a screen shot from the Console app (in the Utilities folder) showing the most recent disc burning tasks including the intial one that failed verification. The highlighted text is my inserted note and not from the Console app. Interstingly it apperas as if iTunes does not perform a disc verify after a burn as the verify task is absent from the Console log.
The Finder preference files can be found at User/Library/Preferences/...
Of note is that none of these discs will work in the internal Superdrive and so I must assume that the internal Superdrive is offcially busted and must have failed coincidentally with my upgrading to Mountain Lion.