SuperSU Errors when rooting Galaxy S3
It turns out I simply had to download a more up-to-date file (which included the Odin executable which runs on the PC, and the .tar that it uploads to the phone) from here, using the table to look up the appropriate file for my device.

For my Samsung Galaxy S3 (GT-i9300) The file was CF-Auto-Root-m0-m0xx-gti9300.zip available from here.