The most common consistency Break I see in Fanfiction is that the writer switches between the kinds of Point of Views. It is so annoying. I already said all I have to say about consistency, so this chapter is just a rehash.
Pick one point of view and stick with it.
If you write first person and need to switch sometimes, try to switch as few as possible. And make it clear whose point of view is written now.
Don't switch the time tense like others do their clothes.
Keep the characterisation consistent.
Keep the lore consistent. Don't say in chapter one X does Y, but in chapter five, X does Z. X does Y, always Y.

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Things I've learned writing and reading Fanfiction! - Fanfiction Writing Advice
FanfictionAround Halloween of 2018, I joined 抖阴社区 for the first time and started writing Fanfiction, and I have to say, not only did my writing change a lot, from the kind of Fanfictions, to my general style on how I write, I learned a lot since creating m...