Let's deal with the reprehensible part first: He refers to a "beautiful half-Indian, half-Anglo" woman from an old western ("Duel in the Sun") and reports a problem "doing some research on the web" (whoa, he was doing this, or his assistant? Oh, sorry). He's bothered, it seems, that he can't use the old term half-breed ("an unprintable slur", good call on that, at least, and it shows implicit understanding of "use versus mention"), but then bemoans the alternatives, with his own choice "just not satisfying", if apparently better than mixed race and such. After Imus, "writers are on guard not to give offense" and he's in a tither about how to talk about racial identity generally. With Barack Obama and Tiger Woods, we assume readers will know something about their backgrounds, so 'of mixed heritage' can work better. Few of us recall Pearl Chavez's 1946 character, so you need a more precise characterization.
In the end, though, most of us are concerned about more than pithiness when it comes to talking about race: He's bothered by the lack of a clear, fixed term when the problem is that we as a society don't currently have a handle on how to deal with the substance. If you're looking for a handy term to let you waltz through this thicket without breaking a sweat, you've really missed the boat.
OK, now to a word: varmint. The hook of course is Romney's gaffe about being a hunter, specifically a "small varmint" hunter. Varmint is native vocabulary for me, but my gun for shooting such things is called a "squirrel rifle". Romney's remark sounds wrong, facts aside: varmints are by definition small. The Oxford English Dictionary on-line gives examples of bigger animals — deer, bear cub, panther, etc., all from the 19th c. — but those aren't modern varmints. Merriam-Webster's definition fits current usage as I know it far better:
1: an animal considered a pest; specifically: one classed as vermin and unprotected by game lawBut the word itself is of some interest: Safire brushes it off as "a dialect form of vermin, rooted in the Latin word for 'worm'". Well, vermin has a variant varmin. That kind of vowel lowering before r is hardly uncommon (see eye-dialect clerk/clark, there/thar, etc.). But vermin is a collective (I can't imagine anybody saying *a vermin), while varmint is a count noun. (Freeman's column is in fact about the rise of "a coffee". And if the green looks like the color of a certain chain's logo, the color palette works better than I hoped.)
2: a contemptible person: RASCAL; broadly: PERSON, FELLOW
More striking is the t tacked on, something dealt with here a while back. Together with the t/d-less forms mentioned there from ads-l (she use to do such and such, etc.), I wonder if there's not a little more of a story in there about where this change occurs: Most classic examples, treated earlier, all end in -s or -sh, but I bet there are more with -n, like varmint. Maybe that's out there in the literature.
Finally, a question: Don't lots of people pronounce this word as varmit? I thought the famous user pictured above was in that category, but if you listen to the sound files here, there's a clear n. Dictionaries seem to give it with an n, but I think hear it often without.