Mountain Lion Installer detects hard drive damage
To fix this I re-partitioned the volume from Disk Utility running off a USB boot volume. This got the volume accessible and responsive again. Then I restored from an earlier Time Machine backup, and proceeded to re-download and run the Mountain Lion installer, this time with no problems.

While it may be faulty hardware somewhere, I can't rule out that a bug or some other interference for the Mountain Lion installer damaged the partition. It has been working fine for days now, and was working fine prior to ML.