Resolving online disuputes well requires judgment, maturity, and a certain degree of empathy... none of which are really `objective' factors. But the more you can found your judgment in objective, verifiable factors, the less you will open yourself to charges of playing favorites, or being a hothead, or letting yourself be swayed by personalities. Any of these can contribute to an unhealthy online environment, so do what you can to put objective factors into place. The Acceptable Use Policy is a primary tool for this.
Copyright and privacy laws as they relate to the Internet are complex and rapidly evolving fields. The authors of The MUCK Manual make no claim to expertise in this area. That being said, a general premise stands: if you have put in place a policy stating the site's position on copyright, privacy, and related issues, and have put in place mechanisms to make players aware of the policy and a way for them to indicate their agreement to abide by the policy, it will be much easier for you to show that responsibility for any illegal acivity that occurs on your site rests with an offending individual rather than you, the site administrator.
A sample Acceptable Use Policy, which may be freely ammended to fit
the needs of your