So far so good. After enabling SMART on the drive in question as per the wiki, then running the test suite, viewing the results gave me a list of result with the following at the bottom.
Warning! SMART ATA Error Log Structure error: invalid SMART checksum
A bit of googling revealed that each disk has a somewhat unique SMART output which needs to be included in the smartmontools database. New disks are added to the project, and the local installation can be updated with the update-smart-drivedb command.
Running this command gave me another error
/usr/share/smartmontools/drivedb.h.error: rejected by /usr/sbin/smartctl, probably no longer compatible
A bit more googling lead me to this site, which has a reasonable explanation of the issue and a possible solution.
The update-smart-drivedb gets the latest drive information from sourceforge.net, but the layout of the site has recently change, breaking the update-smart-drivedb script.
The quick fix is to edit the file and change the url that is used to grab the updated drive configurations.
Using your favourite editor, open the file /usr/sbin/update-smart-drivedb and update the line
The update-smart-drivedb should now work correctly.
Back to working out if the disk is actually the problem...