Uhh, I think everyone who is active on the blog has seen the movie, so I'm just gonna give my thoughts on Alec's question (which had occured to me as well):

My little brother's explanation of this problem was that maybe Burgess developed concrete plans to lead Anderton to the hotel room. Had these plans been carried out, then Anderton would have killed the guy -- but it turns out that they are unneccessary because Anderton decides to go find the guy anyway (and Agatha sorta gives him directions to get there). Still seems kinda floppy, but that's the best we could think of. As for what those plans might be, maybe dropping Anderton some note saying "I have your son" and giving him the room number in the hotel would be sufficient.

I had a couple of other minor questions that might be answered if I saw it again, such as: why doesn't the eye surgeon do something horrible to him? How does his wife get his eye? I also agree that they could have been more subtle about the scene where his wife finds out -- I mean, she doesn't even need to find out right then, she can just be really suspicious and then go get Anderton.

As for Noah's question regarding the ending, at first I thought it could have ended either where he starts to arrest Crow or where he shoots him -- but if it had ended with him shooting him, we would have been really confused as to why he had been set up (since we would have known that he had been set up). If it had ended with the arrest, I think we would have been dissatisfied because precrime would have continued and we already know that there's something very wrong with it.