Risks of upgrading from OS X 10.5.8 to 10.6.3
As with any major change to an OS I'd recommend taking a backup of the machine before the migration. TimeMachine is the Apple's built in backup software. If your upgrade goes poorly you'll be able to restore from a TimeMachine backup without supplying OS media. To ensure that you have a complete and consistent TimeMachine backup I'd recommend running the backup with all applications closed. Preferably get a few different backups so you have multiple points to roll back to.

Secondly, I'd check the installed third party applications and their compatibility with 10.6, some applications might not support 10.6 and will need to be updated to continue to work. You could install a third party program that will track application that will inform you of application updates. I use, and would recommend, AppFresh for this purpose.