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an error in action, calculation, opinion, or judgment caused by poor reasoning, carelessness, insufficient knowledge, etc.
a misunderstanding or misconception.
to regard or identify wrongly as something or someone else:
I mistook him for the mayor.
to understand, interpret, or evaluate wrongly; misunderstand; misinterpret.
to be in error.
and no mistake, for certain; surely:
He’s an honorable person, and no mistake.
Contemporary Examples

Make no mistake, this is a regime that is deathly afraid of its population.
Iran’s Revolutionaries Are Winning Reza Aslan June 8, 2010

He was not very funny, for starters, which while not a crime is a mistake for someone whose profession is making with the laughs.
Conan Vs. Jay Choire Sicha May 1, 2010

When I was in my mid-twenties, I made a mistake that seems unimaginable to me now.
The Progressive White Guy’s Guide to Privilege Andy Hinds September 5, 2014

A French Embassy employee tearfully admitted that “brothers at the intelligence ministry made me understand my mistake.”
Iran’s Chilling Show Trials Gary Sick August 13, 2009

Brutality must be rejected as a “mistake,” but simultaneously preserved as a possible policy option.
John Brennan’s Tortured Defense of the CIA’s Torture Program Shane Harris December 10, 2014

Historical Examples

“I trust that there can be no mistake upon that point, at least,” replied he.
The Martins Of Cro’ Martin, Vol. I (of II) Charles James Lever

Without reasons I was sure of, you know, so there could be no chance of any mistake.
The Spenders Harry Leon Wilson

I was sure there must be some mistake on your part, that you had confounded him with some other person.
Monte-Cristo’s Daughter Edmund Flagg

“Nothing, only you locked the door by mistake,” said Ben, coolly.
Brave and Bold Horatio Alger

“But it is a mistake,” cried Don Cornelio, rubbing the cold sweat from his forehead.
The Tiger Hunter Mayne Reid

noun
an error or blunder in action, opinion, or judgment
a misconception or misunderstanding
verb -takes, -taking, -took, -taken
(transitive) to misunderstand; misinterpret: she mistook his meaning
(transitive) foll by for. to take (for), interpret (as), or confuse (with): she mistook his direct manner for honesty
(transitive) to choose badly or incorrectly: he mistook his path
(intransitive) to make a mistake in action, opinion, judgment, etc
v.

early 14c., “to commit an offense;” late 14c., “to misunderstand, misinterpret,” from a Scandinavian source (cf. Old Norse mistaka “take in error, miscarry”), from mis- “wrongly” (see mis- (1)) + taka “take” (see take (v.)). Related: Mistook; mistaking.
n.

1630s, from mistake (v.). Meaning “unintended pregnancy” is from 1957.
In addition to the idiom beginning with
mistake
also see:

by mistake
make no mistake