Some RL examples...
Officers can hold people until the person's identity is verified to the OFFICER's satisfaction. In 2072, there's probably a bureaucratic formula they have to follow, though.
Shooting people is usually a bad idea, even for Lone Star. Remember Murphy; he's an employee in every company at the lower levels. One, there's always a chance of some media group deciding to do an 'expose' of bungling cops, and guess who the lucky guys to be fired to satisfy public demands will be? Two, you never know really who you might be shooting. Sure, that trog ganger might be up to no good; but he might also be someone's CI (confidential informant). Drekking off a high-level detective/supervisor is not a good career move. Three, it's in everyone's best interest (everyone being Lone Star) for Lone Star not to be known for shooting people who don't resist with guns/lethal implements. Sure, you may have smartgun(tm) links; but do the gangers shooting back? And if Lone Star gets that 'gun-happy' rep on the streets, you can bet everyone will be taking shots. Whereas if it's known that they beat you up, but don't shoot you, (unless you get stupid) a lot of street types will run but not shoot Stars. This makes for happeir co-workers.
That said, there's a lot the business of justice can do. Getting convictions for crimes is good; even if the guy you nabbed isn't guilty of that particular car-jacking, he's guilty of something, right? Find it and book him. Set goals for your officers; 'We need 50 muggers busted by the end of the month'. Encourage (and reward) 'creative' methods of solving cases and proving guilt (as long as it can't be proven the officer did anything wrong). Illicit entry? No; you saw a crime in progress. Profiling? No, you witnessed the perps committing a traffic violation. And have the superiors get on the officers about complex, long cases. "Look, it's better to have 5 convictions for burglary in a month than one homicide conviction in three months. Until this guy kills someone important, stop wasting time on the investigation."