Schools should not be responsible for punishing students for anything outside of school unless the issues are brought into school (i.e. getting picked on inside the school because of an online post, etc.). I believe if it is outside of the school, it should be the parents' responsibility to monitor and punish their students. Especially with the lack of proof most schools will have with actually proving a student said "x,y,z." Parents should do their part and be setting good guidelines and examples for their children. The positives of being anonymous online are quite clear -- you are anonymous -- you can join anonymous groups, talk about things with others that you would not regularly because of embarrassment or fear. The negative is that you can say a lot of bad and harsh things without any retaliation.