"mistake in choosing" is correct and usable in written English.
You can use it to indicate that a mistake was made in the process of selecting an option. For example, "George realized that he had made a mistake in choosing the wrong phone plan."
She said that she had made a mistake in choosing me for a husband.
Russia's leaders are making a mistake in choosing a different strategy.
Probably I made a mistake in choosing some players but my experienced players performed very badly in the second half.
The questions were more antagonistic, including one about whether the Labour party had made a mistake in choosing him as leader rather than his brother.
People at the program now say that if there was any mistake in choosing John for the police station it was in not including Rigoberto Torres in the commission, or in John's not insisting that they include him.
The pressure group Democracy for America suggested that Obama and Biden had made a mistake in choosing a moderate instead of judges that might have fired up the Democratic base.
Worse, Gilbert has noted that these mistakes of expectation can lead directly to mistakes in choosing what we think will give us pleasure.
"Finally Getting It Right: From Addictive Love to the Real Thing" (1994) offered strategies for avoiding making the same mistakes in choosing a partner that previously led to misery.
It is to be expected that they will make some mistakes in choosing friends and, hopefully, they'll learn important life lessons about friendship along the way if parents are there to guide them.
"I appreciate your willingness to admit that this was indeed a real plane crash, and that a mistake was made in choosing to use it".
He notes, "the biggest mistake people make (in choosing jobs) is to follow the traditional 'plan then implement' model...but it typically doesn't work.
