Chaos Is Very Good is composed of these, not surpringly. And yet, the Mayor's ghost talking makes the whole thing seem sane and sound in comparation.
Many stories have Cid Highwind from Final Fantasy VII randomly complain about people interrupting The Dukes of Hazzard... and then the show is never mentioned again and most of the time the plot continues as usual.
Bart the General, despite making little sense to begin with, has a few scenes like this, such as one when House climbs a water tower and gets his cane broken by an icicle, and a scene where Barton wakes up in an underwater vault with a strange gauge.
Subverted in Latias' Journey with the Berry Stoo fight, the RPG arc, and the battle between the Pokérangers, Team Rocket and the Tyrantron. Not only does Ash get a rematch with Stoo later on, but Mewgle becomes The DragonThe Man Behind the Man, and the origin of the Pokerangers becomes an important plot point.
Played straight when Giovanni's body (working for Deoxys) is trying to interrupt Rayquaza's resurrection and stumbles onto the set of a game show for no good reason.
Not exactly, Copernicus(the ghost) is mentioned in the following scene, by characters who had NOT been there. He is one of the guard ghosts, and a character from another fanfic author.
In the EvangelionGag DubEvangelion: ReDeath, Pikachu attacks NERV. However, the following scene acts like an AMV for Pokémon set to the AC/DC song "Big Balls", and there's not much of a focus on Pikachu, but rather James, another character from Pokémon. After the "AMV" is done, ANOTHER random anime is introduced — Tenchi Muyo!! The cast of Tenchi Muyo! is quickly killed off by Pikachu, and the plot returns. ...yeaaah...
One of Stephen Ratliff's later Marrissa Picard stories, 'Winning Love By Daylight', has this bizarre (even by Ratliff standards) scene where Jay Gordon and the resident psychiatrist Martin are talking about Marrissa's problems in a restaurant when the narration casually mentions a monster walking in to the place. Just as suddenly, two of the 24th Century's version of the Sailor Scouts show up (please note that outside this scene, Ratliff's stories are Star Trek: The Next Generation fanfic and don't usually cross over with Sailor Moon or anything else) — one of them being a half-Klingon girl. The two vanquish the monster and leave. Jay and Martin comment on the weirdness, and then it's never mentioned again.
Actually, it's probably best that you don't think about My Immortal period.
My Immortal is full of them. Dobby is one.
The hacker's chapter and Draco's suicide are two of the most egregious examples.
While Naruto Veangance Revelaitons is not very coherent, the dream sequence Ronan has in Chapter 47 in which he, among other things, comes face to face with the author's stepbrother, is one by the author's own admission.
In chapter 1 of Frigid Winds And Burning Hearts, Princess Luna knocks a bowl of soup into Prince Blueblood's face. There is then a brief, inexplicable cutaway to the bowl of soup's dying thoughts, as it hopes to have earned a place alongside Sir Lint-a-Lot and Rocky in Inanimate Object Heaven. To say this is out of place in a story that takes itself so seriously it's painful is to make a gross understatement, and this is never mentioned again.
Turnabout Storm has a reference to the infamous Dark FicCupcakes. It involves a creepy zoom in with eerie music playing and the background turning red, only for then to have everything turn back to normal without a word about it ever being mentioned again. To make things even weirder, the reference is triggered by a discussion about freaking LADDERS.