Is the mispronunciation due to an accent, or a incorrect idea of how the word/words are supposed to be pronounced? The latter would irk me, & I would definitely correct, but if it’s because of an accent, then I think you should let it go.
So like, if he’s a bit of a bumpkin & saying “im-pordant” instead of “imporTant” (for example), it’d be a bit nitpicky to correct him over that, & I get why he’d be sensitive. But if his mispronunciation is affecting the clarity of what he’s saying (say, he’s pronouncing “ideally” as “idly” or something) then I think gently correcting him is okay.