Oliver Putnam didn't have move out of apartment when he did. He could have waited until a court ordered eviction was rendered, which could have taken weeks to happen.
Sazz Pataki says she can still smell in the glasses that the victim and his likely killer drank before the murder. This would mean that they hadn't been washed and should have the killer's fingerprints on it. It seems odd the police didn't have enough sense to collect them for evidence.