As a character study, Mystic River is awesome, some of the best acting (Penn and Robbins) and directing (Eastwood) I've seen in a while,...but as a murder mystery, it sucks.
The screenwriter doesn't want us to know that Dave didn't do it, so he leaves out extremely important details about him.
The writer makes the cops idiots by having them ignore important evidence in order to make Dave look guilty.
You don't need to believe me: I'm right, anyway.