Continuity mistake: During the opening party, extras are recycled - in particular, a man with a white fedora appears multiple times, sometimes with shades, other times not. (00:02:00)
Continuity mistake: Humphrey writes the various names on his whiteboard. In the close-ups that immediately follow (and in those later in the episode, but days have passed meanwhile so it's more understandable) the letters have partially faded. (00:14:15)
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)
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: 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: 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: During the rendition of the Commissioner's movements with the glasses, he says in a faraway shot that the governor "was standing with Andy Hammond." Before it cuts away from this shot, you can see JP handing the appropriate photo to Goodman seconds before it actually happens. (00:09:50)
Continuity mistake: Commissioner Selwyn Patterson holds the glass and bottle at a different height in the wider shots (fingers are at the champagne level in the glass) and in close-ups (glass about an inch fuller). (00:03:50)
Answer: There's probably no particular reason. Sets and props on long-running TV shows often change as needed and for various reasons throughout a series run.
raywest ★