Continuity mistake: When Humphrey explains the findings of the post-mortem, he speaks waving his right arm around - in front views, because it's the left when the camera is behind him. (00:14:40)
Continuity mistake: When Florence answers Humphrey's question about the french word for "affair", she is holding her pen in hand with the thumb at the bottom. Next shot, with the enraged president standing up, and she's placid in a different position, her hand turned to support her chin. (00:22:20)
Continuity mistake: Dwayne hands DI Humphrey Goodman the telephone with the pictures of the drill holes; in close-up, Goodman's fingertips are barely against the sides, while in the other shots the fingers wrap more closely around the device. (00:23:55)
Continuity mistake: Humphrey tells Florence to stop the car and points at Andy Hammond. As we see him through the dirty window of the Defender, a couple (woman in pink tee, man in pattern blue and white shirt) passes by him. When Humphrey opens the car door, they are in the background, far away. Next shot when he begins his short lived tailing, and those guys are again passing the politician by. (00:35:35)
Revealing mistake: When Humphrey checks out of the mail from the dating website at the end of the episode, behind the window of the mail client, there's a fingerprint file with the name "Adam Frost" and a 2014 sampling date; it's a file recycled from two seasons before, 3-4. (00:49:55)
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.
Continuity mistake: In the intro, Zoe appears all of a sudden by the stage entrance; the other two models were on the runway with nobody there before the cut. (00:00:15)
Continuity mistake: Sadie Mernier tells the police about the victim's stalker. In close-ups, her large hoop earring is caught between her hand and her face. Camera further back, and the earring is on the outside. (00:09:35)
Continuity mistake: When Humphrey turns towards Florence to mutter instructions about checking the case with the UK police, Joséphine Jobert's hand is positioned on the top side of the notepad, and in a different position at the cut. (00:09:50)
Continuity mistake: Humphrey and Florence are checking out of the crime scene the morning after. When Florence says "Also, if she's telling the truth" the pen did a 180° turn in her hand; it had the ballpoint up, now it has the cap. (00:10:45)
Continuity mistake: Rosey Fabrice visits the police station the morning after the murder. Dwayne puts his moves on her and places his hand on the back of her chair, but in the close-ups his arm and hand are simply not there. (00:12:10)
Continuity mistake: DI Humphrey Goodman writes the name of the victim on the whiteboard, in a close-up. He then starts enumerating the suspects, but the name changed penmanship - look at the odd shape of the E linked to the previous letter, or the suddenly shallow M. (00:13:50)
Other mistake: Florence closes her notepad and puts the cap back on the pen when Dwayne just begun telling everyone what the Gendarmerie reported about one of the suspects. She has no way to know by that point what Dwayne is about to disclose, and that Humphrey is about to leave with her. (00:17:05)
Continuity mistake: Florence walks towards Goodman reading the post-mortem results; before the cut, you can see Kris Marshall's chin leaning on his right hand, but he has the opposite hand up and the right one down when he comments on the 'small mercies'. (00:23:20)
Continuity mistake: Florence advises Humphrey to "just be yourself." The slice of lemon is on (her) left side of the glass. Reverse shot and it's the right side, then it is back on the left side, where it remains for the rest of the scene. (00:28:35)
Continuity mistake: Humphrey sat down with the photographer, and asks him about the incident that bankrupted his previous agency. He says "Of course I would", scowling and putting the right hand on his left arm. Reverse shot, and his hand is on his knee. (00:34:05)
Continuity mistake: In an uncharacteristic display of authority, Humphrey orders Sadie Mernier to go back to her chair and answer the rather personal questions. She walks back with her shades in her right hand, and in the shot when she slumps back in the chair, the sunglasses are in the left. (00:37:10)
Continuity mistake: When Humphrey sits at the killer's table, they have the right hand on the left elbow in the first shot, both arms forward in the next. (00:45:55)
Continuity mistake: Dwayne's bottle of Etensel is facing opposite directions when he tries to act as if he didn't see his boss embarrass himself at the bar; the label faces the camera when the camera is to his right, and to his left. (00:50:35)
Continuity mistake: After the mishap at the bar counter, Humphrey reunites with Dwayne and Florence. He puts the glass on the table when he sits down, but in the next shot he's still holding it and only after a while he puts it back down. (00:50:40)
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.