You're not necessarily wrong, but I've got a couple of things which may interest you to hear about that particular case, the man who was pushed over and subsequently died.
You're very much correct that the officer in question was wrong to do what he did, and that the coroner was biased (and he probably ruined a lot of lives being biased, but that's a whole other thing) but I think the smear campaign idea you brought up needs more attention, because it runs both ways.
I watched the video again, and there's no reason that the officer should have shoved the guy, but he did. He might have done it to make himself feel powerful or something along this lines, but what he didn't do was hit him whilst he was down, he didn't hit him with a weapon, he just shoved him out of the way, and the guy was pushed to the floor. He wasn't trying to kill that man. He made a hideously bad judgement call but obviously didn't intend to harm the man in such a way that he'd die.
That's easily manslaughter, but it wasn't intended to be. I don't agree with the way the police and media handled what happened, and I've heard just as much about how terrible the officer in question is as I have about the victims drinking habits. They're both getting the same treatment now.
This is going through the proper channels and courts. It's getting investigated and slow as justice might be, it's getting done. You can't say it's not fair, because it looks like the officer is going to be punished, and because it's all been so public, it's not going to be light.
As for positive experiences with the police, I've not had many experiences at all with them, but when I have had to talk to the police, they've been very courteous and respectful towards me. I have had various relatives in the police force as well, one being a detective in the Met. You learn very quickly that there are two sides to every story, and a story about the police doing something wrong sells well.
As for positive experiences with the police, I've very glad that they've caught the murderers who killed the women in my area. That's very positive.