Only humans err (cf. St. Augustine: Errare humanum est > Alexander Pope: “To err is human, to forgive divine.”). If we attribute error to animals, it is because we are grounded by our habits of thought, our native penchant for the anthropomorphization and metaphorization of everything. When it comes to language, the least interesting domain within this sub-category of human behavior is what linguists call speech errors and are typically on about, namely slips of the tongue (lapsus linguae), Spoonerisms, and the whole panoply of performance errors that are easily correctible and, indeed, usually corrected on the spot (including so-called Freudian slips).
A mistake is an error or fault resulting from defective judgment, deficient knowledge, or carelessness. It is also a misconception or misunderstanding. The etymology is from Middle English mistaken ‘misunderstand’ < Old Norse mistaka ‘take in error’ < mis– ‘wrongly’ + taka ‘take’. Error is from Middle English errour < Old French < Latin error < errāre ‘wander’. From the perspective of Latin, then, the ultimate meaning involves ‘wandering’, alias straying, deviating from the right path. Compare this ur-meaning to that found in the root of the Russian word for error, viz. oshibka, a deverbal noun: –shib– means ‘throw, hurl, sling’, and o– is a prefix with ‘mis-‘ as one of its senses, e. g., ogovorit’sia ‘make a speech error’ < o- + govori- ‘speak, say’. The modern verb for ‘err’ is oshibit’sia, which originarily must have been derived from something like ‘mis-‘ + ‘throwing’, i. e. ‘missing the mark’. In Japanese, to extend the comparative scope, the quotidian word for error is machigai, where the element ma means ‘space’ or ‘time’, and chigai is the deverbal nominal stem (< chigau ‘differ’) meaning ‘difference, divergence’; hence error in Japanese is ultimately, as in Russian, something like ‘divergence from the right point/mark in space (or time)’.
The upshot––linguistic, moral, and pragmatistic––of this natural history of (the words for) error is support for Charles Sanders Peirce’s IDEA––also to be disinterred from the etymologies of the words right and wrong––that “men and words reciprocally educate each other; each increase of a man’s information involves and is involved by, a corresponding increase of a word’s information . . . My language is the sum total of myself.”