Goddamn it, shut up, shut up, SHUT UP!
It’s bad enough when we’re nitpicking, but when we’re nitpicking but also joking and being enjoyably witty so that I feel compelled to keep reading despite my inherent impatience with both the inevitability of this thread’s direction and its content…ARGH!
Had to get that off my chest. Carry on.
You are not the grammar police. You’re not even the fucking grammar crossing guard. The phrase one “another thing coming” is not grammatically incorrect. It’s not even really idiomatically incorrect, which is probably what you meant. I have always heard, and read, the phrase as “another thing coming”. Though no great user of the phrase, this interpretation is infinitely more sensible to me. As such, I will continue to use it, no matter that some pocket tyrant thinks it proper to regulate my word choice. ‘Another thing coming’ makes perfect sense, feels better in the mouth, and seems to be the preferred modern usage.
Oh, and about that Webster cite, read this page. Specifically the last part of that central entry.
And while we’re at it, the phrase is, “I couldn’t care less.” To say you could care less implies that there are other things that take even lower precedence on your list of things to care about, whereas by mocking the thing about which you don’t care, you really wish to imply that it is, indeed, the last thing about which you care, i.e., the last thing on your list, not next-to-last or higher.
Got it?
Esprix
Ahh, but Esprix, both are in acceptable use now, just as ‘thing’ and ‘think’. Stephen Pinker, author of The Language Instinct, claims that the ‘incorrect’ usage of ‘I could care less’ has taken on a sarcastic tone. [sub][sup]I wish I could give an exact quote, but like an idiot, I sold the book back to the campus bookstore after I was done with my linguistics class. Alas.[/sub][/sup]
Therefore, both phrases are similar, with a small difference in connotation:
“I couldn’t care less what you think of me.” This is a direct dismissal of a person’s opinion.
“I could care less what you think of me.” Not just a dismissal, but there are snide undertones as well, adding a mocking tone. Falls under the same heading as ‘That’s sooo original.’ Complete with eye-rolling smiley. 
Trucido’s on the right track. Nitpicking common usages of language is, in the end, futile. You will be assimilated. 
Yes, it is.
*Who really gives a rats ass!
No, really.
[sub]*That is the correct phrase, isn’t it?
it needs an apostrophe.
no, really it does
I received an email from someone about a week ago in which the author suggested I had another “Thingk” coming. Should I summon the thought police, the grammar police, the spelling police, the intellect police, or should I just go over to his house and get medieval on his ass?
b.
Pfeh, I say. I fail to see how “thing” makes more sense than “think” in the context of “If you think that, you have another think coming”; i.e. “if you think that, you will soon be forced to hold a different/opposing thought.” “Thing” is simply etymological drift, which also gives us such gems as “for all intensive purposes”, Esprix’s “I could care less”, and (my favorite) “supposably”.
Which is not to say that there is anything wrong with the evolved forms; such is the way language develops. And you have every right in a free society to use them. But I still reserve the right to kvetch about it as well. 
If you think that, your result will be quite different from the one you were expecting.