I meant to post this a while ago, but hopefully more people have seen it now so they'll know what I'm saying. If you haven't seen the movie yet, don't read this! It might give something away.
So I found this loophole (I think) in the logic of the movie. Maybe I missed something.. anyways, here it is:
The only reason he went to the apartment was because he saw it in the precogs. But the precogs wouldn't have seen it unless he knew about the apartment and wanted to go there. So the precogs would've had to have been programmed to see that so that HE could see it so that he could do it.
So there's no way he could've killed that guy. They wouldn't have foreseen it if he didn't know the guy, and he couldn't know the guy if they didnt' forsee it.