This is a rather complex issue. I really think the police should be held accountable for any intentional mistakes or even those that could be prevented. But if a police officer is in fear of his or her life and hasn't had enough training, then punishing them isn't going to solve anything.
Yes, the police should have to pay for their mistakes. If police officers know that there is a financial disincentive to them acting wrongly, there would be more of a reason for them to act responsibly. The taxpayers should not be punished financially for the wrongdoings of police officers who misbehave.
Police should be be held accountable for their mistakes more than most other jobs because the mistakes made by the police can mean life changing events for the person on the other side. Police force need to know that they can't just do things without any thought on how it will affect others. By holding them accountable, it will reduce the number of mistakes they make.
Working as a police officer is such a specialist role that you cannot afford to make any mistakes, a bit like doctors and fire fighters. For this reason they should be made to pay for their mistakes because they did their job wrong and it can have dire consequences. The punishment should be appropriate though, otherwise if you came down hard on every office who made a mistake nobody would want to become a cop!