A big example in Child of the Storm, which started out as a light-hearted family fic with liberal sprinklings of humour - albeit with a warning from Word of God that it would get steadily darker as the HP books did - and one that emphasised the Harry Potter side of the crossover, the Marvel contribution being restricted to the MCU prior to Iron Man 3. Then, chapter 11 introduces HYDRA, their chief weapon the Winter Soldier and villainous Ensemble Darkhorse and Knight of Cerebus Gravemoss and the story shifts gears, steadily developing into a complex and intricately plotted Mega Crossover with a penchant for truly epic battles.
A major example in Yognapped: the original instalment switched through plot conceits with no concern for the holes it caused, featured laughably one-dimensional villains, and had chapters less than half a page long. The major focus of the series — the conflict between the three gods and Lewis's slow descent into moral questionability — didn't come up until halfway through the second installment. Cue retroactive rewriting.
Saki After Story has this in its first chapter, even though there are only two as of this writing. In the first chapter, mahjong is seemingly treated as a two-player game (Saki and Teru face each othernote This is disregarding how, in canon, as Teru is her team's vanguard while Saki is her team's captain, they would never face each other in the team tournament, with Saki winning 112,000 points to Teru's 110,000), and Saki and Nodoka are on a Last Name Basis, as opposed to the First-Name Basis they adopted in the training camp between the prefecturals and the nationals, at the end of the first anime series.
Fanfics in general fall into this - as is the case with professional authors. Many fanfic writers' earlier fanfics might not resemble their later fanfics in terms of plot or format. This is understandable as fanfic writers often get tips from reviewers on how to improve, and will often use them.
Fairly noticeable in The Vinyl And Octavia Series. The first story in the series is more or less a straight adventure story. Although there is comedy, the story itself is not one, unlike the rest of the series. There's no sexual tension between Vinyl and Octavia, and aside from a few mentionings of shipping, there is no hint that the two have feelings for one another. Finally, this story is around forty-thousand words long and spread out over multiple chapters, unlike the rest of the series, which are all one-shots (with the exception of Vinyl and Octavia Have Multiple Dates, but that's still only two chapters and is in fact shorter than some of the other stories).
The Infinite Loops were codified by Saphroneth but made by Innortal. Thus, Innortal's loops will occasionally do things deemed impossible in later loops, which is usually Hand Waved by the fact that they were the first loops and the restrictions didn't exist yet.
Enter Ken Finlayson: There are entries from Ken's journal which do not appear from later stories; Ken is stated to have been born in Leeville, Ontario instead of Casablanca, Morocco; Ken seeming to be actually crazy... Although that could just be a case of Character Development. There are also moments when Norrisville is stated as being in the state of New York, predating the revelation that Norrisville is located in some New England state.
The original first few chapters of Hit List were less polished than the rest of the story and read like a straight-up High School A.U. with the Legend of Zelda cast, as opposed to later chapters treating the games as canonical precursors by having Link, Zelda, and Ganondorf as the reincarnations of the games' characters (the writing was fixed when the author did a rewrite). The sequel, From the Dust, uses more direct references to the games, with the characters getting magical items and entering actual scenarios from the games. This stands in contrast to Hit List, which kept everyone in the more realistic setting of a high school, had the characters make use of mundane items to defend themselves, put much less emphasis on interacting with plot elements from the games, and had no magic or past-life interactions until Link and Zelda fight Ganondorf.