In a very simple sense, you use a term when you employ it to mean something; you mention a term when you talk about the termness of the term, or if you quote someone using it.  So for instance if you say that someone called someone an ugly name, you put that ugly name in quotes. Thus, he said "word" is mentioning; those people are words is using.

This is germane to something Jay Nordlinger of the National Review Online has recently written.  In a nutshell, in a recent post he used a derogatory term for Mexican immigrants.  In a follow up post, he claimed it was obvious that he was mentioning.  His defense, however, is weak.  Here's the original remark.

In today’s Impromptus, I have some comments on Chief Justice Roberts, including a gibe. (Columnists must gibe.) A reader writes, “I fear he has grown in office, and will keep growing.” Yes, that is a fear. For political newcomers, we’ll need a brief history lesson.

During the 1980s, Tip O’Neill and other liberals said, “We were hoping that Reagan would grow in office, but he hasn’t grown at all.” What they meant was, he had not shed his small-government principles and his hawkish views. He had not accepted the post-LBJ state, and détente. He had not learned to love Big Brother. He was still clinging to guns and religion, so to speak. He was as provincial, blinkered, and right-wing as ever.

Truth is, some conservatives lamented that he had indeed “grown” in office. He had gone out of his way to accommodate liberals and moderates, and to accommodate the Kremlin. He was raising taxes, spending like crazy, welcoming wetbacks, pursuing arms control. One common cry from the right was, “None of this would be happening if Ronald Reagan were alive.”

Here is his defense:

What has gotten knickers in a twist is that word “wetback.” What should have been clear is that I was reflecting a certain mentality: the mentality of Reagan’s critics, some of them, at that time. The angst over tax deals, amnesty deals, arms deals, etc.

I have no doubt that most readers knew what I was doing. But I guess you have to issue these little “clarifications” for the benefit of the dim.

Look: I am not a politician. I’m a writer. And if you don’t like what I write — for heaven’s sake, there are 8 billion others you can click on. I would further say to the complainers, using a phrase I’ve never liked, frankly: Get a life. Get a frickin’ life.

One more word: If people wet their pants on seeing the word “wetback,” this country is as far gone as the most pessimistic and alarmist people say it is.

Two more words: Good grief.

I find this very sad.  In the first place, Nordlinger's defense fails.  There is no distance between the people (not him allegedly) who use the term "wetbacks" (see, quotation marks are easy to use!) and Nordlinger.  Indeed he counts himself among them.  Second, he claims to be a writer, but then he whines about people who criticize what he writes.  That's what people do to writers.  Writers write, they get a reaction, they deal with it.  Nordlinger instead goes ad hominem on the people who think his employment of this offensive term offensive.  What is therefore most sad about this response is that Nordlinger bothers (like so few actually do) to address criticism of his view but then fails to learn from it or take it seriously. 

Maybe this really was a failure of the use/mention distinction on Nordlinger's part.  It's so easy to cop to that.  He could have simply added that he should have made it clear that he was mentioning "wetbacks" and that it was a term he finds inappropriate.  But he couldn't do that, because it was central to his point about how Reagan was justifiably criticized from the right.