There's multiple things going on here. We've seen use of communications channel A to organise harrasment on channel B - which is hard for B to stop ("brigading", gamergate). Gamergate escalated into real-life death threats against its targets. We've seen on-platform organisation of harrasment of people on and off the platform (this is ultimately what got Milo banned from twitter). We've also seen "news" organisations get into finger-pointing and condemnation of random citizens (e.g. Daily Mail outing a teacher as trans, resulting in her suicide).
We've seen the legal system get involved clumsily. There's seemingly no middle ground between "joke in poor taste" and "arrested for bomb threats" (#twitterjoketrial). Occasionally people resort to libel law, and even more occasionally the less powerful, famous and obnoxious person wins (Katie Hopkins vs. Jack Monroe).
People are I hope aware of the ability of abuse reporting systems to themselves become channels of abuse. Facebook's real names policy is exploited by anti-trans campaigners to force people off the platform, for example. Anyone should be aware of the risks of automated threshold systems being abused: if all you have to do is get 100 accounts to press "report abuse", that will be abused very quickly.
Local standards also present problems. Do we really want to go along with e.g. Pakistan arresting people for blasphemy?