I'm trying to think through this from a legal perspective. If I'm going from store-to-store around town, my understanding is that police are allowed to watch me and even go into the businesses and ask questions or pull security footage without a warrant. The information they gather is circumstantial and probably would not hold up in court, but they can use it as grounds to get a warrant. Let's imagine a different cas…
In US v Jones, a GPS tracking case, the minority opinions were basically concerned with the fact that the GPS monitoring continued over a wide period of time, covering a wide area:
In his concurring opinion, Justice Samuel Alito wrote with respect to privacy: "short-term monitoring of a person's movements on public streets accords with expectations of privacy" but "the use of longer term GPS monitoring in investigations of most offenses impinges on expectations of privacy"