I have some system that predicts homicides and their perpetrators. It makes a prediction: Alice will kill Bob tomorrow at 9am.
I wait and see.
It turns out it's right.
It makes another prediction: Charlie will kill Doris tomorrow at 1:30pm.
I wait and see.
It turns out it's right.
I let this run until I get enough data to make a statistically valid assessment of it's accuracy and find that it's 99.95% accurate in that the event it predicts actually takes place and the perpetrator is the person predicted.
The rate of false positives will be 5 innocents predicted to commit murder for every 9995 guilty people.
This how the predictions are presented in the film.
The problem is that it's akin to arguments for an enlightened dictatorship. And sure, you can test that the guy is enlightened before you elect/revolt/coup/whatever to put him in charge. The question though is the same: will the same apply for the NEXT guy? Will it even still appy next year?
The problem is: ok, so you've tested and proven that in the year X, guys Y and Z are prescient. Fine. I'll grant you that, for the sake of this exercise.
But then you stop testing it altogether, when you start stopping the predicted events from happening. And you don't really know any more if the event is actually stopped by precognition or it wouldn't have happened in the first place anyway.
What if some of your precogs go schizophrenic and start having visions that have noting to do with the future? What about the NEXT batch of precogs? Etc.
At some point you stopped having any confirmation that the system even works at all any more.
The thing is, we have safeguards against the police lying or being schizophrenic or just have a batch of incompetent cops. Because they're required to present evidence that someone else, hopefully less invested in having another solved case on their resume, can independently verify and confirm that yeah, it adds up to that guy being guilty.
You DON'T have the same safeguards when essentially your standard of evidence is literaly something from Family Guy: "I call to the stand the ghost who can never lie. But only I can hear him." Except in this case you don't even know if the case you're judging is imaginary or not, so it actually one-ups Family Guy for absurdity.
Hell, even with video, what about cases of mistaken identity? They happen IRL all the time. But IRL you have safeguards like having to show that the guy you arrested was actually there, or if someone else saw him in another place alltogether. But when you deal with stuff that only one guy saw in the future, how do you prevent that?