You have to think about your goal. Is your goal to get the teacher to correct their mistake and move forward? Or is it to boost your ego?
If it's the former, it's probably better to approach them later, in private, and point it out politely. They will correct the problem next session, or send out an email between sessions.
Either that, or be very polite, e.g., "Excuse me, Mr. Smith, but you wrote down <wrong stuff> there. Why isn't it <right stuff>?"
If you say, "Mr. Smith, you're wrong. It should be <right stuff>, not <wrong stuff>" you are strictly speaking correct, but you'll humiliate them. It feels good for your ego -- I'm smarter than the teacher! -- but probably won't advance the class.
This isn't about the "sorry state of education," it's about knowing what people feel when you blurt shit out in class.
Why is it the student's responsibility to protect the teacher's ego?
Here is the admittedly unusual way in which I look at it: In most cases, the school system (including the teachers) is implicitly claiming that students are better off in school with them than anywhere else. When a ludicrous claim like this is being made and enforced, I don't see why they should be cut so much slack.
It's not the student's responsibility to protect the teacher's ego, it's the student's responsibility to be reasonable. Standing up and yelling because the teacher forgot a semicolon in some example code, for instance, is a waste of everyone's time, not just the teacher's.
Your somewhat extreme example notwithstanding, are you saying it's unreasonable for a student to point it out when a teacher is giving incorrect information to the class?
I'm saying "It depends." My experience with that behavior indicates that it's usually counterproductive- either nitpicking like my previous example, or axe grinding that isn't really helping. Think an Ayn Rand follower interrupting a class on Marxism every few moments.
The problem, really, is that it's impossible to make a fully qualified statement and still be engaging. As a speaker, you have to skip over some detail somewhere, thus there is always going to be a place to jump in and act an ass.
That's depressing. That's what education is supposed to be about (rather than blindly accepting incorrect facts).