I haven’t seen the movie so I don’t know the details of how the system is meant to work. Yet if the psychics and police are able to predict murders and then prevent them, the murders cannot be predestined. If God or Fate or whatever foreordains that a murder is going to happen then by golly it’ll happen no matter what mere mortals do to try and prevent it.
If it seems that psychic information is preventing murders then I see only two explanations. Either the psychic visions are bogus and the whole thing is a big scam, or they’re visions of a possible future that can be averted through human action. Neither scenario negates free will (although neither requires it either).
Getting back to the OP, if it’s all a big scam then the ethical problems are obvious. I guess one might eliminate murder through such a scam, if it made people too afraid to even think about murdering anyone. However, it would seem that the only way to make the scam convincing enough to produce that effect would be if the goverment went around framing innocent people for imaginary future murders and then executing them. (I take it from other posts that something like this did happen in the movie?) This could be seen as a form of “taking one life to save a hundred”, but even if one has no objection to this in principle there’d be no guarantee that the numbers would actually work out that way. There’d be no guarantee that the scam would successfully deter any murderers at all. The government would also be guilty of a massive deception of the general public.
If the visions are genuine but of a possible rather than predetermined future, the questions becomes “Is it okay to kill someone if they might kill others?” I think the answer to that depends on how detailed our information is and how certain we are of the possibility. If the police act on highly suspect information then things are hardly better than they’d be if the government started executing people at random. So let’s say we’re quite certain that the prospective murderers at least possess genuine intent to kill. Under ordinary circumstances, I think that if someone learns of a murder plot they have an ethical obligation to do what they can to prevent the murder from taking place. This would remain true if the plot were an idea in someone else’s mind uncovered through supernatural means. But do you kill someone just because you know they’re planning a murder?
Ideally, one would prevent the murder in the least harmful manner that would still be effective. I think the reasonable approach would be similar to what Bryan Ekers suggested. Take the prospective murderers into custody, find out who they want to murder and why, and then take steps to both protect the intended victim and try to work the problem out non-violently. If the prospective murderers could not be reasoned with then imprisonment or psychiatric confinement might be justified. I can’t see similar justification for killing them unless the future visions reliably indicated that this was the only way to keep them from carrying out the murder. Doesn’t seem like a situation that would occur very often, though.
It’s even less likely when we get into unplanned murders. A psychic vision detailed enough to be certain about would probably contain enough information to allow police to prevent the murder-inspiring situation from occurring in the first place. There would be cases where nothing more dramatic than a well-timed phone call or other minor delay could disrupt the chain of events leading to the murder. At the extreme end, the cops could show up in time to tackle or stun the prospective murderer and save the day. Some kind of follow-up counselling might be necessary (help the husband deal with his jealousy issues, convince the wife to be faithful or file for divorce), but solving the problem with killing seems like…overkill.
It seems to me that the only justifications for a “kill first, ask questions later” policy would be not ethical, but practical or financial. It might be easier and cheaper to kill someone (or put them in the freezer) rather than give them years of state-sponsored therapy. But if we’re willing to go that route, it seems like a short but slippery slope to deciding that it’s easier and cheaper to forget both the legal system and this psychic mumbo-jumbo and just kill anyone who seems the least bit suspicious. Heck, why not cut the Gordian Knot and end all crime permanently by killing everyone?