L.C.
Oh, I don't ignore it. It does, in fact, drive me insane and I do all kinds of things. Some out of practicality, some out of frustration. I have:
Explained that I expect more of him because he is older and needs to hush
Explained that his sister needs to be free to discover the world just like he did
Made my older child leave the room
Done the exact same thing to him - corrected every minute error of fact or grammar in every single statement that came out of his mouth until he wanted to scream and then said, "Doesn't feel good to be treated like you're dumb, does it?"
Enstated the "He who picks the fight, gets the consequence" rule.
It's better, but we still have our days. How about you come back on and tell us what works, or better yet, make a teaching DVD out of it and sell it and become a millionare and the title of Genius of This Century.