I have the same problem. I teach at a state university and I'm occasionally addressed as "Dr." even though only have an MS, unlike everyone else in the department. Similarly, I'm occasionally addressed as "Professor", even though I'm only a lecturer. I'm a stickler about not inflating my resume or my credentials, so this makes me uncomfortable, just as it does you.
Usually I'll offer a correction but sometimes not. With my students, I specifically tell them at the beginning of every quarter that I do not have a PhD and am not a professor, explaining that other people have earned those titles, I have not. I'm a lecturer and they should call me Nicole. Most do that, though some will still call me "Professor", usually, I suspect, because they've forgotten my name or because they follow the casual convention among students of calling all their instructors "Professor". I'll generally let that slide though if they do it in a one-on-one conversation, I may gently remind them, "You know I'm not really a professor, right?"
With others, whether I offer a correction depends on context. If it happens in conversation, I always offer a correction. If it's on a notice or a poster or something else that might be seen by others, I always ask for a correction (which doesn't always happen, to my discomfort). If it happens in a forum of some kind where a speaker has referred to me as "Dr." in front of a lot of people, I'm always uncomfortable but always let it slide at the time, rather than correct the speaker in front of others, possibly making them uncomfortable as well. But I may look for a later opportunity to offer the correction privately.
With emails, if it's simply an automated email (even sometimes from my own department), that's easy: I ignore it. With other emails, it depends on whether I have to reply or if I expect to have more contact with the individual. If yes to either, I always offer a correction and, as with my students, ask them to call me Nicole.
Anyway, that's what I do. YMMV.