It depends upon the person and how obnoxious he/she is being.
I once was discussing a meeting location with a coworker.
Him: Meeting A is in the same room that Meeting B is in.
Me: No, Meeting B is in Room X.
Him: No, it's not.
Me: Yes, it is.
Him: No, Meeting B is in Room Y.
Me: I've been attending Meeting B for the last few months. I think I should know that Meeting B is in Room X.
Him: Oh, did it change?
Me: Why are you arguing with me about this?
Him: I'm not arguing.
Idiot. Just made himself look really stupid...again (seriously -- meeting I'd been attending for the last few months, multiple times a week, which he hadn't attended that entire time, and he was going to argue with me over where it's located???).
Years ago, I had another coworker do the same thing. We kept going back and forth and, finally, this happened:
Me: I'm not going to argue this point with you anymore.
Him: That's because you know I'm right.
Me: No, I don't. I think it's a waste of time to keep going over this with you.
Him (in an offended tone): Oh, gee, I'm such a waste of your time!
I said nothing, shrugged and went back to work. I think our other two coworkers just cracked up. Frankly, I didn't care that he was offended. He certainly wasn't going to be left with the notion I stopped arguing with him because I was conceding he was correct.
Bottom line is -- if I think either a) the person is worth correcting or b) the topic is worth correcting, then I'll speak up. Otherwise, I'm not going to waste my time and, if someone asks me, I'll admit it's not worthy my effort to address (Crazy Older Sister is one of those I will no longer waste time or effort on).