Episode #1.5 - S1-E5
Other mistake: An enraged Richard tries to get the drawing board in position making a bit of a ruckus. If you look at the board, it has names and pictures on it; they are from the future, since they are part of the 6th episode, "An Unhelpful Aid", evidently filmed earlier, out of order. (00:07:25)
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)
In the Footsteps of a Killer - S6-E7
Trivia: In the close-up of the diary of Julie Matlock, you can read in the column to the right of the page with the mysterious number 19871 a name; Agnes Dahan. It's the name of the production buyer of the episode, and long time staff member of the show in production and art department. (00:20:20)
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.