Yes, even your boss is human and sometimes makes mistakes. If it's a mistake that could impact the company's business and/or its customers, you should definitely try and do damage control, even if it means telling your boss he/she is wrong.
And yes, it can usually be done without damaging your own career. Here's how:
1. Be discreet.
Never call attention to your supervisor's mistake in front of other people, whether they are superiors or subordinates. And definitely don't talk about it behind his/her back. Causing embarrassment won't get you anywhere, except possibly out the door. Instead, ask for a couple of minutes private discussion, or send an email.
2. Be respectful.
Nobody likes to be corrected. Don't make the situation even worse with a know-it-all attitude. Start your comment with a "compromise" phrase that allows your boss to acknowledge the error with dignity. "Correct me if I'm wrong, but I think you used last year's production figures instead of this year's." "I'm sorry, but we can't really guarantee delivery by tomorrow."
3. Be a questioner.
Instead of making a flat statement of "you're mistaken," put it in the form of a question. "Just checking, did you really want to copy the client on this email?" And after you've received revised (or confirmed) instructions, always say "thank you."
So you see, with a little tact you can sail smoothly through what could be a very sticky situation. This tact would also include choosing a time to confront your boss when he/she is in a good mood, and not in a hurry.
Handled right, a problem can be made to disappear without hurting either your or your boss's careers. Even better, your tactful support just might pay off in a stronger relationship with your boss. And who knows where that could lead!