Continuity mistake: Jack and Humphrey are following the taxi in Jack's grey car, the registration number is DG60 SGY when they start following the taxi and LN63 FEJ when they park in front of it. (00:14:50 - 00:16:25)
Continuity mistake: When Martha says "Yes" to Humphrey, the waiter in the background has his hands free. She kisses him in the next shot, and in order to clap with the others the waiter has to put down two wine glasses he was holding. (00:49:45)
Continuity mistake: At the pub towards the end of the episode, Jack brings a glass of rum to Dwayne. He hands it to him with his left, but you can see in the shot when he begins to get seated that it's the right arm that he has extended. (00:48:10)
Continuity mistake: Up to the point when Martin West says he took the gun to 'impress the lads', Florence has her hair to the right of her face going in front of the shoulder. New shot, and there's much of it combed back, and it keeps going back and forth until it's again all in the front in Florence's next close-up. (00:26:15)
Continuity mistake: The detectives are discussing the presence of the cufflink. Humphrey asks if "He's taken his own life in remorse", and the camera cuts to the deceased. Notice an iPhone on the desk by him. A moment later, the phone rings and Humphrey has to search the victim's pockets to come up with the phone. (00:04:55)
Continuity mistake: In the intro, Dominic Green greets the client from Saint Marie. A few people are passing by the car when he opens the door, but when he closes them those people vanished in thin air. (00:01:55)
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.