Just for clarification...we know that they arrested or caught SOMEONE for the killing, right? It was implied when the new detectives brought up that maybe they got the wrong person, I thought.
In the "current" timeline, they mentioned they had made an arrest in the past. But the two detectives seem to have re-opened the case because there was another similar murder. Remember the picture of the murder they showed to "older" mcconaughey toward the end of the pilot? That was a new murder - implying they had arrested the wrong person.