Continuity mistake: When the episode begins, Jessica is having a meeting with Sally Wilson, who hangs a bag over her shoulder. A shot later, her bag is down and she is hanging it again.
Audio problem: When Buck walks to the bar downstairs and meets Mrs. Oates, the sound of their footsteps is that of tiled floor, but they're walking on a rug.
Factual error: When Buck's body is found, his blood is red when it should be brown due to oxidation after how much time has passed.
Answer: In a flashback scene, it was shown that he had a violent temper, so it stands to reason that he finally killed her in a fit of rage.