From a brand spanking new mac purchased 3 weeks ago with leopard installed immediately after unpacking, here are the issues I've seen.
1. Mouse freezes on wakeup from sleep (Probably a USB issue)
2. System hang while playing DVD in front row
3. Intermittant loss of audio, need to restart coreaudservice
4. syslogd thrashing CPU 100% usage, needed to delete log file and reboot
5. Safari hung on many occasions
6. iPhoto quits unexpectantly on import of photos
7 iPhoto got into a funny state asking me each time I opened it, to finish importing files, when I selected yes, it just quit. I had to go into the iPhoto files and delete a bunch of stuff to make it stop.
8. Dashboard widget locations get messed up
9. Inability to unmount network/dmg's reboot needed
All this in 3 weeks of usage...
I had a mac-mini a couple of years ago running tiger and it seemed much more stable than leopard, though it was a slow machine.