Who did it? Are you sure?

I wondered that about "the soldier". Did he do it and his commanding officer (or whoever that was) wanted to make sure it was covered up, or were the bar stories he was telling related to something he and other soldiers did to a girl overseas? A couple of things point to it being him - Woody's line about "somewhere in a bar, somebody will say something" (paraphrasing) and the way that "the soldier" came into the shop and messed with Mildred. Of course, the former could be coincidence, and the latter could just be a sicko getting off on the tragedy of others which happens to mirror an act he carried out somewhere else.

Actually, there is one line stating, "There was no match to the DNA." So the new police chief makes that statement, but the entire scene is rather odd. One would think that the lack of a match would be the most compelling evidence, but most of the scene focuses on the fact that the guy was out of the country. Based on the guy's version at the bar, he was the only rapist; so presumably the only DNA on her would be that of the rapist. (I'm excluding the possibility of a third person's DNA being on her; i.e. someone other than her and the rapist/murderer.) And presumably some foreign DNA was found on her (else there would be no purpose in obtaining the suspect's DNA). So the only logical possibilities are that this guy was not the rapist (in which case he was just talking trash, as was suggested in the movie), or he was the rapist but someone was covering up for him. I think it was probably just some random person (i.e. not the dad or other characters in the movie), and like the police chief said, some day somebody will talk and the case will be solved that way. (And if the soldier did it, then he would not confront the mother in her shop. That's just way beyond stupid.)