I think there are a bunch of things to consider:
Was he malicious and trying to denigrate you, or was he thoughtless?
Why, even if the thought occurred to him based on whatever was said just before this, did he think it was a good idea to put you down in front of his father? Has he done this before? Not just with his father, but with other people (neighbors, people at parties, whatever)?
Why, when you raised the issue and indicated that you were hurt, did he stick to his position and not, in your words, "back down"? Were you clear that you were looking for a retraction or at least an apology? Does he normally take a strong stand and never, ever apologize or waffle or change his mind? If so, wouldn't that be what's bothering you, and not just this one episode? You said this: "He offered to start pointing out to me when I do something that he thinks shows my lack of common sense. You know, to "help" me." That sounds pretty stubborn and arrogant, to my mind.
Maybe you and he have different backgrounds, but it sounds to me like you aren't feeling very confident. If he said you were intelligent, why didn't you hear that? Was he saying that you are smarter than he is in that way, and was he, perhaps, building up his own shattered confidence by saying that at least HE has common sense (like street smarts).
I think, if you took the time to say, "occasionally I make mistakes or have an accident, but doesn't everyone?" then you are highlighting some insecurity there.
I think that joking about divorce is a really bad idea, at least in the middle of an argument. Those are statements that are hard to take back, and it's not really "fighting fair."
Sounds to me like both of you would rather be right than reach an accommodation or understanding, and that concerns me a lot more than this one episode, thoughtless as it was.