I'm in a strange position on internet 'abuse'. Obviously those who make repeated threats directly to another person are guilty of harrassment and threatening behaviour, and should be prosecuted, but take for example someone tweeting in general something like "ugh I wish Vanessa Feltz would die already".
That could be construed as a 'death threat' or trolling or abuse. But it's totally something that shouldn't be prosecuted. In that instance someone would have to search for Vanessa Feltz's name to find it, it's not a direct threat and it's a celebrity person being bitched about in extreme proportion.
And then there's racism and homophobia... again, I don't think these should be punished by law. We cannot truly call ourselves a society built on free speech if we do. I'm all for people reacting to racists and homophobes with outrage and publicity, because that can lead to them losing their jobs and basically ruining their lives which they totally deserve. But criminal prosecution? Nah.
But it's such a thin line online... at what stage does a threat reach harrassment? Three tweets? Five tweets? Tweets over weeks? Months? (I'm of course just dealing with Twitter here, take Facebook to be 'wall posts' or 'messages' instead

) Some small part of me thinks that harrassment shouldn't be a crime either because if we're going to
truly and fully live by free speech then I should, by right, be able to tell people "I want to kill you"... because it's thought, not action. But obviously intimidation and mental abuse is a real phenomenon and I would, as would anyone, report someone to the police if they got too harmful and worrying.
It's just difficult to monitor, really, and especially when those in power are entirely oblivious to how the internet operates.