Sounds like a bug. Do you have the latest updates for Logic 8 and SL?
To be honest, I haven't installed Logic 8 on my Snow Leopard system. I prefer to use it on 10.5.8 and Logic 9 on 10.5.8 and my 10.6.1 systems.
I have heard of the quit issue. By all accounts it is more of an inconvenient issue than a serious bug. Make sure you save your project and close it and then force quit Logic 8:
and Force Quit Logic 8 is one way to do this.
What I do, is have one External drive with 10.6 and my main drive with 10.5.8 (or the other way around) - that way I have the best of both worlds :)
I also hear that 10.6.2 is in the pipeline to be released sometime in the near future. Don't know when, but perhaps that may help... or hopefully Apple will release Logic 8.0.3 that resolves the issue?