I have always interpreted that as meaning Superman is deputized. That is not the same as saying he is exempt from the same restrictions (beyond jurisdiction) that other law enforcement officials are subject to. Thus, he can apprehend criminals just like a regular beat cop of FBI agent, but every time he uses his x-ray vision without a warrant or scares someone into confessing a crime or gets a confession without reading the criminal his or her rights he is exceeding his authority and acting like a vigilante.
I would have to agree with you. At the height of his relationship with the authorities (in the Silver Age and Bronze Age, I guess), if he did not follow the correct law enforcement procedures, how would the accused ever be convicted in a court of law? The case would be thrown out, surely?
Although, if you read some of those old comics, it's plain that Superman got away with a lot of things that a police officer would never get away with, eg. grabbing someone and effectively arresting them without reading them their rights or even saying the words, "I am arresting you." Imagine how many people were assaulted by Superman, technically speaking. But I don't have a problem with that. I trust Superman a lot more than I would trust the average cop, and maybe in the Silver Age the authorities understood that Superman is the most honest and dependable law enforcement officer of them all -- I certainly did. Imagine Superman giving testimony in a court of law: if he said he saw you commit the crime, your goose is cooked. Superman would never lie about something like that, and everyone knows it. Even more than being "deputised," the Man of Steel obviously had some sort of dispensation that an ordinary officer of the law could never have. And rightly so.