An "ad hominem" is a kind of argument, that is fallacious (though, in some contexts, may actually be fairly reliable: more on that in a moment). The argument has the following structure: X asserts Y; you attack X to undermine Y, e.g., you argue that because X is a certain kind of person, Y is false and/or ought not to be believed. (Note: the fallacy, strictly speaking, would be to conclude from facts about X that Y is false; concluding that Y ought not to be believed based on an attack on X can be reasonable, a point to which we'll return.)
While it is true that many ad hominem fallacies take the form Leiter suggests, this is certainly not true of all. An ad hominem occurs whenever one substitutes an (irrelevant) characterization of someone's reputation, abilities, or character where a (relevant) argument would be required. Ad hominem fallacies are fallacies of irrelevance: they do not apply to the argument at hand, but are mere distractions from it. I don't understand Leiter's parenthetical remark; it doesn't matter, as far as whether something is an ad hominem is concerned, whether the conclusion is that Y is false or that Y ought not to be believed; in either case, if there is a substitution of personal characterization for relevant argument, there is an ad hominem fallacy. In cases where argument is called for, the only case I can see in which an attack on X would be relevant (and thus not a fallacy) is a case in which Y is put forward on X's authority, and therefore depends in some way on X's credibility or reliability.
Leiter is right that an insult is not necessarily an ad hominem fallacy; some insults are put forward as insults under conditions that don't require argument. Likewise, it is possible to phrase premises or conclusions of relevant arguments in insulting ways; this is not ad hominem, either. Interestingly, Leiter's example of an ad hominem that might serve as a good epistemic rule of thumb is not an ad hominem (unless it were used in a place where it just didn't apply). This is because it is actually part of a general argument about credibility or reliability; it would then be applicable nonfallaciously (and thus not as an ad hominem fallacy) in any case in which the warmonger's credibility or reliability were genuinely in question. Since an ad hominem fallacy is a fallacy of irrelevance, any time in which a person's character, reputation, or abilities is genuinely relevant to the argument, characterization of that character, reputation, or abilities cannot be an ad hominem fallacy.
One of the difficulties with ad hominem fallacies, as with many other informal fallacies, is that people can at times reasonably disagree about whether a particular case is genuinely an instance of the fallacy. This is because identifying the fallacy requires an assessment of whether argument is really required. If we are going to ask ourselves, for instance, whether Leiter in using the label "InstaIgnorance" to refer to InstaPundit is just a description (however insulting) or a case of poisoning the well (i.e., pre-emptive ad hominem), we would have to look at each particular case to assess relevance, and whether argument was required instead. There can potentially be disagreement about whether argument was required. For instance, someone might say that, given that Leiter is a well-known academic, and given that he does work in philosophy, one can reasonably expect him to focus more on clear reasoning, which would increase the number of cases in which argument could reasonably be demanded. Leiter's own defense does not, I think, work; the issue for ad hominem is not whether a description is true or false, but whether it is relevant. That "InstaIgnorance" is an apt name for InstaPundit has no bearing on whether Leiter's uses of the label are cases of ad hominem fallacy. (Ironically, because of this irrelevance Leiter's defense of his use of "InstaIgnorance," in which he argues that it is not an ad hominem fallacy, is itself a case of an ad hominem fallacy. Were Leiter simply arguing that InstaPundit should be called InstaIgnorance, it would not be; but as a defense against the ad hominem fallacy of irrelevance, it commits that fallacy. This is true whether one agrees with Leiter's actual argument or not; one can have a sound argument used in a fallacious way.)