Episode #1.8 - S1-E8
Factual error: In the close-up of the password from Antigua and Barbuda, the nationality listed is "Antiguan", while as redundant as it seems, official passports from that country list it as "Antiguan and Barbudan." It also has no place of birth listed at all. (00:24:20)
Continuity mistake: When Aunt Mary is writing on the whiteboard at the hospital, the word "killed" changes style between shots. (00:31:40)
DI Jack Mooney: Strictly speaking, paradise is a state of mind. You know that, right? I mean, the dung beetle - very different idea of paradise, doesn't he? (00:48:25)
Trivia: A bit of the episode has been cut for the streaming releases; at the end of the scene with Humphrey taking Martha's luggage, he would make a date with her for the next day, to cook dinner for her at 8. This has been eliminated probably because it created timing issues with 8 PM being too well lit (in contrast with the supposed timing of the murder) and the ending takes place at Catherine's for a cute drinking scene anyway. (00:22:50)
Question: Why did the cord on the wall phone in the police station change from straight in the early episodes to coiled later?
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 ★
As long as such changes aren't an obvious continuity mistake (e.g. changing multiple times during a day), one can just assume the change happened in-universe as well. Things do get broken or updated occasionally. It adds a bit of realism, in my opinion.