Your argument for total police surveillance of public space is flawed on two points:
1) Your comparison between yours or your neighbour's private recording, and blanket systematic surveillance is not valid. It is not valid because of the difference in scale. When you commit a crime, or a good deed, scale always matters. Kill a person, vs. a million, and you will see very different reactions. Same thing if you give a homeless person a coffee, or feed million hungry.
If we were to allow blanket police surveillance of all public space, with automatic face-detection, and what not of other technologies they deem useful, we'd end up in a 1984 / Kafka world of tyranny. Only from the false positives alone, there would be a prison population dwarfing the US' current for-profit "correctional" facilities.
2) Secondly, you seem to believe that the police can be trusted and uphold the law and code of conduct to the letter. Spend any time searching (YouTube or Google) for police brutality and mistakes, and you will find that the opposite is true. And no, this is not that case of "a few bad apples", it is a natural effect from the abuse and corruption of power.
Any power or privilege will be abused by a not insignificant number of people it is given to. It is unfortunately human nature. The police force is no different, and that is why there is thousands on thousands of videos showing the police acting like thugs all over the place. They cannot be trusted, and we must seek to limit their power, not expand it.
So coming back to the original problem of camera surveillance, the case in the article was a typical example of abuse of power by those who were entrusted with it. Give out more power, and this effect will only multiply. Nor are technological solutions to this social problem adequate or possible; they never are. Instead, we must simply avoid putting up cameras everywhere.
To summarize: All power will be abused. Therefore, we must grant only as little power as possible to any system or person in control, lest they abuse it. That's a basic property of any modern democracy, and the police force is no different.