Factual error: Celestial navigation can determine one's position on the earth's surface to within about one mile, not precise enough to give the location of a buried treasure. It also requires more than a sextant. It requires tables published in a nautical almanac (which is updated each year), charts on which to plot lines of position, and an accurate chronometer that is set to the precise time at the Prime Meridian (Greenwich Mean Time).
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.
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.
Visible crew/equipment: After Seth drives Jessica downtown, lights, crew, and filming equipment are reflected on the car window.
Continuity mistake: When Jessica is having dinner, his glass swaps between full or almost empty depending on the shot.
Audio problem: Several times during the episode, when someone is walking on a rug, the sound of footsteps is that of a hard tiled floor.
Visible crew/equipment: When the cop grabs the coffee pot, a filming crew member with blue trousers is reflected on it.
Character mistake: When the corpse is taken out of the water, he moves his mouth.
Audio problem: The cabin floor is carpeted, but the footsteps heard are of a hard tiled floor.
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.