Next I tried rebooting, holding C to boot from install disc. Everything seemed to go well and I told it to install to a spare partition, preserving the Leopard installation so I can run some comparison tests. The install disc seemed happy with this arrangement and I've seen other people confirm that the Snow Leopard disc will let you do a clean install and not just an upgrade from Leopard. It proceeded to install Snow Leopard on the spare partition, but gave up after a few minutes claiming "Install failed: the installer could not copy the necessary support files".
I rebooted again into Leopard and this time it could see the install disc so I ran the installer. Everything seemed to go fine, but then the remaining time jumped from 35 minutes to 54 minutes and the disc began to start and stop spinning. Then it abandoned the install with the error message; "There is a problem reading the Mac OS X Install DVD. Carefully clean the disc and try again."
Close inspection of the disc revealed no marks, it was fresh out of the packaging, so I tried again with the same result. Leopard's Disk Utility says the disc is fine but a few more attempts saw it fail again and again. As a test I even backup up Leopard using SuperDuper and then tried to upgrade Leopard to Snow Leopard, but the install still failed. I decided the disc must be faulty and put in a call to the Apple support line.
After 10 minutes on hold I explained my situation and the help desk agent agreed the disc seemed faulty. He also confirmed that I wasn't the first person he'd spoken to today with a faulty disc. A quick Google search reveals other people have had the same problem - although this disc fault is confirmed by the Disk Utility.
According to the help desk agent, Apple is completely out of stock of Snow Leopard discs and he had no idea when more will be in stock. His only advice was to call the store where I bought the disc. I did this, just before closing time on Friday, and was told new stock wasn't expected until at least Wednesday.
If you find yourself with a faulty Snow Leopard install disc, you could be in for a long wait.