Cases where "mistake" and "error" are not interchangeable
Are there cases where error and mistake are not interchangeable?
Solution 1:
In statistics, an error is the amount that a measurement deviates from the 'true' value. Even if no mistakes are made in measuring (that is, all the right methods are used, and used correctly), there might still be error due to limited accuracy of the measurement tools, random fluctuations in the system under consideration, etc. The words are clearly not interchangeable in this context.
Solution 2:
One case where they are not interchangeable is in computing where we write error message but not mistake message.
Generally speaking however, error is more formal than mistake. In technical contexts, a mistake happens because of human action, judgement, opinion or decision, while error has no such connotation and can be interpreted more broadly.
Solution 3:
Even outside of computing, mistake generally aligns the error as the fault of the person who caused it, while error means it wouldn't have mattered who was involved — it was likely to happen regardless.
Solution 4:
In the context of computer programming, mistakes are made by human beings making decisions, but errors can be caused by all kinds of faults, not just decision-making faults. For example, a file can be full of formatting errors, but those errors wouldn't constitute mistakes in the computer context unless a person had typed in the file by hand.
Solution 5:
They are not interchangeable in idioms such as in error, trial and error, or error of one's ways.
I must say (though Jasper Loy beat me to it) that computer terminology seems to be more intolerant of replacing error with mistake. A fatal mistake, for instance, is not the same thing as the programming term fatal error.