There are already two great terms with similar meanings that have become widespread:
• Jumping the shark (from Happy Days)
• Nuking the fridge (from Indiana Jones and the Crystal Skull)
Both refer to the moment when a series completely loses the plot and the viewer suddenly realises that something he or she once loved, something once brilliant, has now, definitively, disappeared up its own backside. "Jumping the shark" refers to a TV series; "Nuking the fridge" refers to a film series.
I would like to propose another, a variation:
• Chasing the pigeon
For me, the moment I saw Lee Adama chasing a pigeon around his apartment in Battlestar Galactica, in a scene that was neither meaningful nor relevant (flashback scenes attempting to add depth of character in the final episode?), I knew that one of my favourite TV shows of all time had lost it. Not only was the scene irrelevant, it was also one of the most tired clichés ever... A bird representing someone or something (Kara) out of reach. It invited an unfavourable comparison to the dove at the end of Bladerunner (and also made me think back to Cavil's speech to Ellen about wanting to smell supernovas or whatever, and how that harked back to "teardrops in the rain" from Bladerunner too - not comparisons you want to invite).
Below is what Ron Moore, the show runner and writer of the finale, had to say about Lee Adama (and by extension the show itself) chasing a pigeon. This is following an explanation of how he was trying to tie up the plot, all the loose ends, and how he was finding breaking the plot "frustrating and annoying":
I went home and had an epiphany in the shower and said, "It's the characters, stupid!" And it really always has been, and I went back the next day and said, "Let's forget about the plot for a moment and just trust that it will work itself out, because it always does. What do we want the characters to deal with; let's talk about the individual stories and resolutions." I just had an image of someone in their house chasing a bird from the room, I didn't know what it meant but it's an image and let's put it on the board.
(Before going any further, yes, I know that writers often have images that come to them that they want to include; I know that writers make stuff up as they go along all the time. That is fine. What is not fine is if the writer includes the image for no reason other than that he likes it, or if the writer cannot tie up or explain within the rules he set up in his fictional universe the stuff he made up along the way. Everyone is entitled to their own opinion, of course, and I know that as many viewers loved the finale as hated it. By anyone's definition, it was not good storytelling, though. Whether the finale as a whole was good or bad is subjective; the way it changed the rules at the last minute and frustrated expectations of explanations is, objectively, bad storytelling. And let me just say that I watched BSG for the characters, primarily. I would have been happy without any of the great mysteries, with just the characters developing and surviving while looking for a new home. But it wasn't me who decided to introduce a lot of mysterious elements and conundrums - I was invited to ponder those questions by the writers; it's a bit late to say "it's about the characters" after you made an active decision to lead viewers down a different path. Well. I could go on parenthetically all day. Let us move on...)
The pigeon thus actually becomes a symbol for a writer making stuff up without knowing where it fits - which is exactly what the writers of Battlestar Galactica did with the opera house scene, Kara's death and resurrection, and Head-Six and Head-Baltar (all of this is well documented, not my personal opinion - search for interviews with Ron Moore; he is very open about how he made it all up and "felt" his way through the story). There is nothing wrong with making stuff up on the fly and later working out how it all fits together later, of course, but the pigeon seemed egregious (the perfect word in the circumstances), and in the end Moore couldn't come up with satisfying solutions to most of what he made up and instead threw up his hands and said, "It's about the characters and God did all the stuff I couldn't think of an explanation for."
"Chasing the pigeon" is thus a nice variation on "jumping the shark": it is the point in a show at which the viewer becomes aware of the writer struggling with the plot to the extent that it becomes so clumsy it feels as though the writer has just given up. It is the point at which the viewer finally loses all faith in a writer who had previously gained his or her absolute trust. It is the point at which the viewer feels cheated by a cheap trick and starts shouting at the screen in disbelief at the hours of his or her life spent in awe at smoke and mirrors; hours that are never coming back.
Battlestar Galactica really chased the pigeon in its finale.
End of line.