This is why we have a nifty little requirement called the Miranda Warning, you know, where the police tell you that you have the right to remain silent and be represented by an attorney. Anything a person says that is self-incriminating cannot be used in a court of law unless they were read their rights.
Personally, all my interactions with police officers have been fairly cordial. I wasn't terribly impressed by the police officer who sat snoring in a chair while supposedly guarding a patient who was in police custody, but other than that I don't have any complaints.