Those are only 'mistakes' if you value human intentions. A grammatical error is only an error because we value the specific rules of grammar we do; it's not the same sort of thing as a false belief (though it may stem from, or result in, false beliefs).

You will see a grammatical error as a mistake if you value grammar in general, or if you value being right in general.

A self-improving AI needs a goal. A goal of self-improvement alone would work. A goal of getting things right in general would work too, and be much safer, as it would include getting our intentions right as a sub-goal.