Continuity mistake: When Ron Moody runs into the sea in pursuit of a suspect trying to escape, he shouts at Jessica to "Get the package!" In the next shot we see Jessica reluctantly follow him in, with a clear waterline from a previous take showing on her dark overcoat/cloak.
Revealing mistake: When Miguel tries to sail away, Jessica runs towards the shore. When she enters the water, Angela Lansbury is replaced with a thinner and younger double.
Revealing mistake: When Santana is killed, a rectangular pad where the arrow was stabbed protrudes under his shirt.
Visible crew/equipment: When Sir John Landry walks towards the fireplace before Jessica unravels the mystery, stage lights are reflected on Jessica's glasses.
Visible crew/equipment: At the beach, when Miguel jumps in the helicopter, two filming lights are reflected on the windows.
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.