Plot hole: The whole plan for the murderer to create a perfect alibi hinges on an incredibly precise timing of the victim's action and bodily reaction to the poison, both out of his control. The Governor needed to shake a lot of hands and deliver a speech without yet dropping dead, and everyone needed to ignore entirely the signs that she was feeling unwell. In fact, she needed to collapse as she was drinking, dropping the glass and doing it somewhere where he could squirt some more of that poison in the glass. He couldn't predict the whole situation with the glasses and the Commissioner that would create the alibi (he leaves the party when refreshments are just being served), but for this unpredictable chance to get an alibi he took the huge risk to carry the whole bottle of poison with him, which the plot never explains why was never found by the police or disposed of.
Plot hole: Why would Sian let Griff into the shower room if she broke up with him the night before?
Plot hole: The shower room door has a lock, that as shown in the denouement the killer never closed - making it fairly obvious that the victim did not lock herself inside the room to kill herself. Another minor but still significant problem with the stratagem used; the killer shot the girl in the chest; even if they didn't do any gunshot residual test on her hand, the trajectory of the bullet still would have proven the impossibility of a suicide.
Plot hole: For the plot to go the way it was described, Newton had to wake up at the right time from his drunken stupor (that for some reason the real killer assumed would last eons), sail his boat, go somewhere at sea to dump the corpse, and then back exactly at his pier in the crowded spot where everyone knows him, and do a thorough bleaching of the cabin, all in less than half an hour, close to 15 minutes since he has then to go to Catherine's, which is half a mile away. So around 10 minutes being generous, for a hungover middle-aged man in bad shape and in shock and be there by 7:30, with the real murder happening around 7 (the wife says at 7:45 that it's been 45 minutes since they heard from him). Of course he also had to do that unnoticed, with no record or witness about a boat sailing in and out within a few minutes at dinner time, and likewise nobody saw the real killer running like mad at the docks - also of course, the whole stabbing was done without a single trace of blood getting on him.
Plot hole: Saint Marie is an island with an astonishing homicide rate, but even considering that, with an a missing person and a phone call reporting a stabbing at the boat of a notorious belligerent drunk, with the same person called by name as the culprit, it's quite inconceivable that in a relatively small town like Honore nobody looked for Newton Farrell and questioned him all night - especially being so easy to find, or even checked the boat. Instead, they are surprised by the bleaching of the deck the day after, proving they did not even look for a moment during the night.
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.