My experiences of the police:
Police attended burglary at home of my then 13 year old self in Northumberland and told my parents that we have a better chance of catching the burglar than they do.
Police car tailgates 18 year old me along a deserted country road in Norfolk and in fear I spead up to get back to the built up area then he pulls me over for speeding.
A friend whose father is a police officer who admits after her parents separate that her dad regularly hit her mother and police had been called at least twice (to her knowledge) to the house. Mother had on at least one of those occasions been pressured to let the matter drop quietly.
Coming out of train station in Derby, DH and I get caught up in horrendous post football match traffic. Cars entering yellow boxes and all sorts. Two Police officers chatting and doing nothing. I ask them out of the window if they should not be doing something to try and direct the traffic flow better. One tells me to shut up and move on or he will pull us over and inspect our car and he "will find something".
A friend of mine joins Leicestershire police (around the time of a lovely BBC documentary showing Leicestershire police officers behaving quite badly although lazily rather than corruptly). During a conversation some 18 or so months later she talks about some kid being arrested and being handled a bit roughly and falling over. I was horrified but according to her it is ok because he was being arrested and people have always "done something" if they are being arrested. We are no longer friends.
We get burgled, my car keys and hence my car are taken. Police are actually initially very attentive because it is part of a widespread luxury car theft ring (only it was my DH's car they were after and they lucked out with my banger). Shortly thereafter my car was spotted by the police who gave chase resulting in my car being abandoned. £150 impound fee later I got it back after a £40 taxi trip since it was recovered to the most inconvenient location possible. Police had told me that when it was found I would be given a choice of where it would be taken probably a location about 2 miles south of me would be best. Perhaps they just thought I fancied a trip to the lovely industrial estates of north Nottinghamshire instead. No explanation ever provided as to why the procedures that I had told would be followed was not.
My dad was beaten up by his partners son after a non-violent argument with his partner (about son's drinking). Police attended and removed my dad from his own home on the grounds of preventing a breach of the peace. Police later advised that they did this because it was easier to remove him (being one person) than the two others (partner and son). Dad spent night humiliated and distressed in police cell.
My DH's mother got a part time job in her 50's as a civilian with a police force. She stuck it out for just over a year before she quit with no job to go to because of the sexist, bullying, ageist, patronising attitude of a "significant minority" of the police she worked for/with.
Nothing really major but enough to have painted a long-term sustained impression of a police force...not to be proud of.
Then take the stuff, the serious stuff you read in the press.