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The phrase "mistake in" is correct and usable in written English
You can use it when you are referring to making an error or mistake when attempting to do something. For example, "He made a mistake in his calculations and got the wrong answer."
Exact(57)
It was a mistake, in my opinion.
"A mistake in the exam?
He made no mistake in the 5,000m.
"Madison made a mistake in their choice.
I've never made that mistake in practice.
(Oops! A mistake in the statistical calculation).
Just a homophonic mistake in translation, really.
Surely, there's a mistake in this name.
"I made a mistake in configuring it".
Well, it was a mistake in hindsight.
A big mistake, in Mr. Tanous' view.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com