My understanding of the Palantir law enforcement use case is that, for example, a gang unit police cruiser going down the street in a bad neighborhood can pick up data from its license plate readers, and be automatically alerted if any passing vehicles are associated with certain parameters.
The plain-vanilla tech solution for law enforcement would be something along the lines of: throw a notification if any of the passing vehicles is registered to someone with outstanding warrants.
Palantir takes it a step further and throws a notification if, say, the vehicle is registered to a known associate of a gang member who is wanted for questioning. This network understanding has to be built on the backend, both by integrating existing data sources and by doing work directly on the Palantir system.
Eventually the cops might start following the vehicle, and pull the driver over for a nominal traffic infraction. At that point, the officer is going to use their Palantir app within their department-issued mobile phone to assist in the discussion with the driver -- for example, if the driver coughs up any names, the officer can type them in to see what comes up in the system.
I'd think that Palantir's defense of this would be something along the lines of, "everyone in this story previously had the right to see every bit of information the system provided, we just made it more efficient". The counterargument would be something along the lines of, the state having such detailed understanding of its citizens' personal lives is ipso facto tyranny.