This is exactly the nightmare scenario we were fearing - and lo and behold, it has already happened: using mass spying data of the NSA to launch fishing expeditions against Americans, and find them guilty of crimes.

You could say "yeah but that data can't be used in Court!". But they can very trivially skirt around that. They don't have to use that data. They just need to use some of that data to show a judge "probable cause" - and BAM: now they have a warrant to legally get access to anyone's data, and that data they can use.

But in practice such process by the authorities makes the "limit" of a warrant essentially useless. The warrant just becomes an extra beaurocratic step that they have to take, but doesn't represent a limit on who they can investigate and how anymore.