Here's a nice article with lots of examples why your fear is not misplaced:
http://www.salon.com/2013/07/07/%E2%80%9Cwhy_did_you_shoot_m...
Thanks. Someone submitted it, being discussed here. https://www.hackerneue.com/item?id=6001843
Here's a documentary you might enjoy: http://www.imdb.com/title/tt2125653/?ref_=fn_al_tt_1
Your fear is generally misplaced, here[0] are police misconduct stats (granted they don't count every single episode of police misconduct) and here[1] are crime stats. Certainly one episode of police misconduct is too much, but it's not nearly as high as crimes the police weren't involved in.
I think sites like HN and reddit showcase police misconduct and this leads to an exaggerated view of how prevalent it is compared to other dangers. It's similar to the MSM and sexual abuse/stranger danger.
[0]http://www.policemisconduct.net/2010-npmsrp-police-misconduc...
The main difference of course is that murderers occasionally go to prison for killing people. Whereas the percentage of police ever actually convicted for committing a crime while on duty is so low they might as well have immunity.
I would take these figures with a grain of salt because I doubt any accurate statistics of police misconduct are kept.
Of course there is a lot more non-police crime than there are reported incidents of police misconduct. What about simple mistakes? I'm not sure if buffoonery is counted as misconduct. What I'm really referring to though, is what is my own personal exposure to risk of harm? I wouldn't be surprised to find that it is more likely that police might kick my door down and shoot my dogs, either by mistake, misunderstanding, or misuse of power, than say armed burglars.
For years I've been skeptical of the efficacy of police tactics and strategy. I'd say that skepticism has evolved to a default of suspicion of any police activity.
I find myself contemplating installation of bars on my doors and windows, security fencing, etc; not for fear of "normal" crime, but of errant police activity. I wish I had some statistics upon which to base that notion. I'm a fairly normal, caucasian, middle-class guy with a wife and two kids, no criminal record; and I am more fearful that I will be harmed by police criminality or ineptitude than by non-police criminals.