You can reconcile the precog predictions by assuming that they see a window in time that is within a set period if time, say one week. The first report sees 6 days forward and says that anderton is going to commit a murder, the second one sees 5 days forward and sees that anderton will get a majority report and not commit the crime, the third precog sees 7 days forward and sees that he will commit the murder but not for the same reasons as the first report. The total of the reports is a majority report of murder, but each part is for a different event.
As for the precogs never seeing a murder since all murders are prevented, the time with Dow resolves this too. If the precogs can only see a week into the future, then their predictions effects almost always like outside the window under which the crime is prevented, only in anderton's case is the report seen so quickly that it can effect the prediction. So they seen forward in 7 day increments, when they publish their reports a murder us going to happen because it is before precime knows about it,after they publish their reports, the crime is prevented and there is no crime to report again. But the window in which they see does not include the reaction of precrime because the reaction still lays outside their window of the Future.