Debatable in Clash of the Elements like most tropes on this page, but while Part 1 has some glaring grammar problems and lack of focus at the beginning, the story steadily improves throughout and becomes rather consistent around Chapter 13... although there are still some grammar issues here and there. However, the beard grows even further in Movie 1, where there is a LOT less grammar mistakes, the battles feel more steamlined, and more details words are used in the narrative to avoid repetition. And finally there is Part 2, which removes nearly all grammar problems, has a fluid narrative with great battles, and a better focus on the characters and villains. It is pretty impressive to read through at that point considering that this is a Mario fanfic and all.
Escape from The Hokage's Hat starts off slow with the first two arcs basically being Recycled Script bar certain details and mostly dealing with the power plays and politicking between Jiraiya and the council. Come chapter 22, the story picks up from the previous rather Filler and isolated feel the first two arcs as more of the world gets involved in the story.
Following Trial By Fire, the Facing The Future Series slowly bean to grow its beard, but it fully grew after A Family Thing where afterwards it introduces many exciting Myth Arcs, the introduction of Danielle as a permanent member of the Fenton family, new ghost powers, a Mysterious Watcher, and a member of the Rogues Gallery performing a Heel–Face Turn, and the series is only getting better from there.
An inversion of sorts occurs with My Immortal. It starts as your classical nonsensical bad fanfiction, but then Tara and Raven have a falling-out, and Raven stops beta reading. At this point, the writing goes from nonsensical to incomprehensible, the "story" loses any kind of relationship to the series that inspired it in a truly dramatic fashion, and the fanfiction itself becomes the disaster that everyone knows and loves.
Although the Tamers Forever Series is an undoubtedly fun and surprisingly well written series, it's still fairly average, until "Forget the Y2K, This is Madness!!", whereupon the series adopts a quality of writing that is on par if not better than that of professional authors.
The Wizard in the Shadows starts out as a straight up Tenth Walker, albeit a good one with a few minor variations, but really begins to hit its stride with the Breaking of the Fellowship, and a following ability to develop its own identity and the author developed and refined his style. This is signified by an increase in the length of the chapters to consistently 3000 words plus.
The Girl Who Loved is a particularly impressive case, as the first few chapters are incredibly rough, with all the problems that it entails, including the usual Flanderization of characters. By about the fourth chapter, the plot begins to develop, most characters become increasingly fleshed out (some don't and a few fanon characterizations are deconstructed), and really hits its stride in chapter 7 and keeps going into its darker sequel, Violence Inherent in the System without losing any of the humor or idealistic aspects.
Child of the Storm started out pretty slow as a simple crossover between the Marvel Universe and Harry Potter. Things started to heat up the moment The Winter Soldier was introduced and never lost steam ever since, by introducing some incredible world building with some fleshed out characters. The fic went on to establish itself as it's own universe rather than a simple crossover fic.
Code Geass Colorless Memories The first 9 nine chapters move slowly and are more about establishing the characters and setting for those who didn’t watch the anime or play the Code Geass Lost Colors where Rai is from. Once Rai joins the Black Knights and the existence of E.E and the Sumeragi's Legacy comes into play, the fic comes into it's own identity among Code Geass Fic's.