Continuity mistake: Backstage, Commissioner Selwyn Patterson reveals to the band members about the message from the victim. The band member in purple has his hand clasped on the beret in noticeably different ways as the shot changes. (00:07:50)
Character mistake: JP says, twice, that the tapes found at the shack are from the same day Jasmine was murdered. Jack then says "June 5th, 1988." But as Commissioner Selwyn Patterson said, Jasmine was killed June 3rd. Jack repeats the date being the 5th later after the visit to Leon. Who's right, is anybody's guess. (00:14:25 - 00:31:20)
Character mistake: Commissioner Patterson begins the narration of the past events with a date, June 3, 1988. It's the day Jasmine died. When Dwayne a couple minutes talks about the band splitting, he mentions that there had been tension before that incident, and says that the band in the summer of 1988 had a tour planned, but Jasmine put a halt to it halfway through. It seems kinda difficult for someone who dies in early June, to put a halt halfway through a summer tour (and that fact being presented as something completely distinct from the person's death). (00:14:25 - 00:16:30)
Continuity mistake: Jack and Florence are talking to Delmar Brown at his bar. Delmar pours himself some hard liquor, puts the glass down close by, and the glass simply disappears for the rest of the scene. (00:19:20)
Character mistake: Interrogating Delmar Brown, Jack mentions to him that "Back in '85, the band went on tour to Europe." But the tour, as established by the Commissioner, Dwayne and Florence's bank statements, happened in 1988. (00:19:40)
Continuity mistake: Time to examine the photo albums just found by JP; Jack has the open folder in front of him. He's about to flip the first page, but in the close-up that follows, he already flipped two; in the following cut he just flipped the first. (00:21:10)
Continuity mistake: Dwayne literally points out of the various pictures with Maya Oprey. JP asks him sarcastically if he wants to do the talking. Danny John-Jules ' hands are joined when he says "If I must", but he has folded arms in the next shot. (00:21:40)
Continuity mistake: The Commissioner visits Jack at his desk to get updates. Jack is busy with the tuning fork; during the sequence it is quite evident that the distance between his hand and the fork is different in the two main camera angles used. (00:32:00)
Continuity mistake: When Jack updates the Commissioner on how slowly both cases are going, his left arm is in a different position on the desk between shots. (00:32:30)
Continuity mistake: Florence is listening to the tape recording with her arms folded. When Jack and Dwayne say that the two on tape had an affair, Florence makes a comment; her hand is raised open or on her upper arm depending on the angle. (00:33:10)
Continuity mistake: At the silver wedding anniversary, Leon gives his speech about what everyone needs to "over-stand"; his hand is on the microphone, off it, on it again, etc.. (00:35:00)
Continuity mistake: Mayor Catherine Bordey approaches Dwayne at the melon stand and talks him into forgiving his dad. During the conversation, she has direct sunlight on her right side (shoulder, face) in the shots with the camera closer to her, and no rays whenever the camera is closer to Danny John-Jules. (00:36:55)
Plot hole: The plot resolution hinges on the fact that the culprit gave the illusion of the door being locked while the lock was already broken. And he did that by jamming under the door a rusty old fork, through the usage of a string. However, this appears really far-fetched to say the least; if the door was obstructed by an object under it, it would have not given way as if the lock was busted. It would have dragged, created a screeching noise and scraping the floor leaving visible marks (which considered it's a locked room mystery, would have been investigated). The person breaking in was Jack, even, who is supposed to be really perceptive and crime-savvy and not the average person.
Continuity mistake: In the episode finale, Dwayne's beer switches hands two times off-camera for no reason and with no visible movement of the actor's arms.
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.