Long as incidents like this, and cops like this,

are handled this way, you'll have lots of people looking at cops with cynicism at best.
A Detroit police officer who fatally shot a sleeping 7-year-old girl in 2010 is being cleared of all charges. The officer has already faced two trials, and officials announced Wednesday that the case will be dismissed.

Officer Joseph Weekley was originally charged with involuntary manslaughter and careless discharge of a firearm causing death – a misdemeanor charge – after fatally shooting Aiyana Stanley-Jones during a botched no-knock raid. The police were looking for a murder suspect who lived on the second floor. The raid occurred shortly after midnight.
... 
Weekley was the first into the home and claims he thought he had run into an empty room. He testified that the grenade was thrown and that, upon regaining his sight, he realized someone was asleep on the couch. He claims that as he pointed his gun at the couch, Jones’ grandmother hit it, causing him to pull the trigger. He plainly told the courts, “It’s my gun that and shot and killed a 7-year-old girl” and denied any responsibility. However, the courts found no fingerprints or DNA evidence that Jones’ grandmother ever touched the gun. Regardless, police protocol is to not have your finger on the trigger.
Possibly just a confused situation.  But some 'WTF?' moments there.  Like that bit about the grenade; is he claiming the grenade went off as or just after he entered the room?  But it gets even better:
During both trials, Weekley and the other officers couldn’t even agree on which officers were engaged in the raid or on whether or not they had seen children’s toys and furniture on the porch before entering. Officers claimed to have spoken to Weekley before or after the raid, and Weekly denied seeing them at all. He testified to moving a child’s plastic chair off the porch, and then denied it later.

So: his story changed, the other cops story changed, and a child is dead and the one holding the gun is cleared.

You think all this doesn't affect how the cops are seen?  What the local citizens think of them?