Could the title of this thread be changed to read "Trademark" instead of "Copyright"? It's a pet peeve, but both concerns go into different buckets.
Regarding trademark issues, I think it really depends on how DEEP the issues are. Just because someone (or many someones') own a trademark, does not automatically entitle them to your domain name. Having a domain name with a registered trademark that's well known (even common law trademarks such as celeb names) can be more than a bit risky though depending on what you do with it. Just ask CupCake Party...
~ Nexus